Cited References by others for Andrew Knyazev

• 1992:
  1. BOGACHEV KY
     ITERATIVE SOLUTION ALGORITHMS FOR QUASI-LINEAR ELLIPTIC BOUNDARY-VALUE-PROBLEMS IN COMPLEX-SHAPED DOMAINS
     DOKLADY AKADEMII NAUK SSSR 322: (4) 641-645 1992
     1. BAKHVALOV NS DOKL AKAD NAUK SSSR+ 312 783 1990
• 1994:
  1. DAS B, STEINBERG S, WEBER S, et al. 
     FINITE-DIFFERENCE METHODS FOR MODELING POROUS-MEDIA FLOWS 
     TRANSPORT POROUS MED 17: (2) 171-200 1994:
  1. BAKHVALOV NS          4 P INT S DOM DEC ME                   197      1991
  2. KNYAZEV AV               19941 P IMACS S IT M                        85      1992
  2. ZIMMERMANN S 
     COMPARISON OF ERRORS IN UPPER AND LOWER BOUNDS TO EIGENVALUES OF SELF-ADJOINT EIGENVALUE PROBLEMS 
     NUMER FUNC ANAL OPT 15: (7-8) 943-960 1994:
  1. KNYAZEV AV            SOVIET J NUMER ANAL            2       371      1987
  3. BAKHVALOV NS
     AN ITERATIVE METHOD FOR SOLVING THE DIFFUSION EQUATION WITH HIGHLY VARYING COEFFICIENTS
     RUSS J NUMER ANAL M 9: (2) 91-97 1994
     1. BAKHVALOV NS IN PRESS NUMERICAL M 1994
     2. BAKHVALOV NS SOV MATH DOKL 44 4 1992
     3. BAKHVALOV NS SOV MATH DOKL 42 57 1991
     4. BAKHVALOV NS SOV MATH DOKL 41 481 1990
• 1995:
  1. BOGACHEV KY
     ITERATIVE SOLUTION ALGORITHM FOR MIXED PROBLEMS FOR QUASI-LINEAR ELLIPTIC-EQUATIONS IN COMPLEXLY SHAPED DOMAINS
     DOKLADY AKADEMII NAUK 340: (6) 727-730 FEB 1995
     1. BAKHVALOV NS DOKL AKAD NAUK SSSR+ 313 777 1990
  2. BAKHVALOV NS
     SOLUTION OF THE STOKES NONSTATIONARY PROBLEMS BY THE FICTITIOUS DOMAIN METHOD
     RUSS J NUMER ANAL M 10: (3) 163-172 1995
     1. BAKHVALOV NS SOV MATH DOKL 44 4 1992
• 1996:
  1. BOGACHEV KY
     Justification of fictitious domains method of solving fixed boundary value problems for quasilinear elliptic equations
     VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA (3) 16-23 MAY-JUN 1996
     
     1. BAKHVALOV NS DOKL AKAD NAUK SSSR+ 313 777 1990
  2. Bakhvalov NS
     Fictitious domains methods for solving elasticity problems
     ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 76: 223-226, Suppl. 1 1996
     1. BAKHVALOV NS DOMAIN DECOMPOSITON 197 1991
     2. BAKHVALOV NS SOV MATH DOKL 44 4 1991
     3. BAKHVALOV NS SOV MATH DOKL 42 57 1991
     4. BAKHVALOV NS SOV MATH DOKL 41 481 1991
  3. Bakhvalov NS, Bogachev KY, Eglit ME
     Numerical calculation of effective elastic moduli for incompressible porous material
     MECHANICS OF COMPOSITE MATERIALS 32: (5) 399-405 SEP-OCT 1996
     1. BAKHVALOV NS SOV MATH DOKL 44 4 1991
  4. Bakhvalov NS, Eglit ME
     Averaging of equations of statics and dynamics of a porous medium made of incompressible material. (Russian. Russian summary)
     Tr. Semin. im. I. G. Petrovskogo (1996), No. 19284--308, 348; translation in J. Math. Sci. (New York) 85 (1997), no. 6, 2415--2427.
     1. Bakhvalov, N. S.; Knyazev, A. V.; Иglit, M. И. A Korn-type inequality and orthogonal decompositions in matrix spaces. (Russian) Dokl. Akad. Nauk 331 (1993), no. 5, 536--537.
• 1997:
  1. BOURQUIN & NAMAR
     Decoupling and Modal Synthesis of Vibrating Continuous Systems
     http://ddm.org/DD9/Bourquin.ps.gz
     Proceedings of the 9th International Conference on Domain Decomposition Methods in Bergen, Norway
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  2. CROS & LЙNЙ
     Parallel Iterative Methods for Large-scale Eigenvalue Problems in Structural Dynamics
     http://ddm.org/DD9/Cros.ps.gz
     Proceedings of the 9th International Conference on Domain Decomposition Methods in Bergen, Norway
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  3. Lui SH 
     Some Recent Results on Domain Decomposition Methods for Eigenvalue Problems
     http://ddm.org/DD9/Lui.ps.gz
     Proceedings of the 9th International Conference on Domain Decomposition Methods in Bergen, Norway
     1. DYAKONOV EG RUSSIAN J NUMER ANAL 7 473 1992
     2. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
     3. KNYAZEV AV SOV J NUMER ANAL MAT 4 283 1989
     4. KNYAZEV AV SIAM J NUMER ANAL 31 1225 1994
• 1998:
  1. Beresford Parlett
     The Symmetric Eigenvalue Problem
     Cambridge University Press (1998) ISBN: 9780898714029
     1. Knyazev, A. 1994. New estimates for Ritz vectors. In Proc. of the Fifth SIAM Conf. on Appl. Linear Algebra.
  2. F Bourquin, R Namar
     A Semi-dual Mode Synthesis Method for Plate Bending Vibrations
     Cont. Math 218 (1998), pp. 384-390
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  3. Lui SH 
     Kron's method for symmetric eigenvalue problems 
     J COMPUT APPL MATH 98: (1) 35-48 OCT 5 1998:
  1. DYAKONOV EG         RUSSIAN J NUMER ANAL           7       473      1992
  2. KNYAZEV AV            SIAM J NUMER ANAL                31      1225      1994
  3. KNYAZEV AV            SOV J NUMER ANAL MAT           4       283      1989
  4. KNYAZEV AV            SOVIET J NUMER ANAL               2       371      1987
  4. Christopher Beattie;
     Harmonic Ritz and Lehmann bounds.
     Large scale eigenvalue problems (Argonne, IL, 1997). Electron. Trans. Numer. Anal. 7 (1998), 18-39.
     1. KNYAZEV AV            SOVIET J NUMER ANAL           2       371      1987
  5. Jean-Luc Fattebert.
     A block Rayleigh quotient iteration with local quadratic convergence.
     Large scale eigenvalue problems (Argonne, IL, 1997). Electron. Trans. Numer. Anal. 7 (1998), 56-74.
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. KNYAZEV AV MATH COMPUT 66 985 1997
  6. D. C. Sorensen;
     Truncated QZ methods for large scale generalized eigenvalue problems.
     Large scale eigenvalue problems (Argonne, IL, 1997). Electron. Trans. Numer. Anal. 7 (1998), 141-162.
     1. KNYAZEV AV            SOVIET J NUMER ANAL 2       371      1987
  7. Andreas Stathopoulos and Yousef Saad;
     Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue methods.
     Large scale eigenvalue problems (Argonne, IL, 1997). Electron. Trans. Numer. Anal. 7 (1998), 163-181.
     1. KNYAZEV AV INT SER NUMER MATH O 96 143 1991
  8. Morgan RB, Zeng M 
     Harmonic projection methods for large non-symmetric eigenvalue problems 
     NUMER LINEAR ALGEBR 5: (1) 33-55 JAN-FEB 1998:
  1. KNYAZEV AV            SOVIET J NUMER ANAL            5       265      1990
  2. KNYAZEV AV            SOVIET J NUMER ANAL            2       371      1987
  9. Zhang T, Golub GH, Law KH 
     Eigenvalue perturbation and generalized Krylov subspace method 
     APPL NUMER MATH 27: (2) 185-202 JUN 1998:
  1. BRAMBLE JH             ADV COMPUT MATH               6        159      1996
  2. KNYAZEV AV            SIAM J NUMER ANAL            31      1226      1994
• 1999:
  1. Zhang T, Golub GH, Law KH 
     Subspace iterative methods for eigenvalue problems 
     LINEAR ALGEBRA APPL 294: (1-3) 239-258 JUN 15 1999 :
  1. KNYAZEV AV            SIAM J NUMER ANAL            31     1226      1994
  2. BRAMBLE JH             ADV COMPUT MATH               6       159      1996
  3. KNYAZEV AV            MATH COMPUT                      66       985      1997
  4. KNYAZEV AV            ETNS                                          7       104      1998
  2. Dobson DC
     An efficient method for band structure calculations in 2D photonic crystals 
     J COMPUT PHYS 149: (2) 363-376 MAR 1 1999:
  1. BRAMBLE JH             ADV COMPUT MATH                   6       159      1996
  3. Bakhvalov, N. S.
     Efficient methods for solving stiff multidimensional multiparameter problems. (Russian. Russian summary)
     Zh. Vychisl. Mat. Mat. Fiz. 39 (1999), no. 12,2019--2049; translation in Comput. Math. Math. Phys. 39 (1999), no. 12, 1938--1966.
     1. BAKHVALOV NS DOMAIN DECOMPOSITON 197 1991
     2. BAKHVALOV NS DOKL AKAD NAUK SSSR+ 312 783 1990
     3. BAKHVALOV NS DOKL AKAD NAUK SSSR+ 313 777 1990
     4. BAKHVALOV NS DOKL AKAD NAUK SSSR+ 319 13 1991
     5. BAKHVALOV NS NUMERICAL METHODS AP 221 1994
  4. Bakhvalov, N. S.; Bogachev, K. Yu.; Metr, Zh. F.
     An efficient algorithm for solving stiff elliptic problems with applications to the method of fictitious domains. (Russian. Russian summary)
     Zh. Vychisl. Mat. Mat. Fiz. 39 (1999), no. 6,919--931; translation in Comput. Math. Math. Phys. 39 (1999), no. 6, 884--896.
     1. ????
  5. Lehoucq RB, Meerbergen 
     Using generalized cayley transformations within an inexact rational Krylov sequence method 
     SIAM J MATRIX ANAL A 20: (1) 131-148 1999:
  1. BRAMBLE JH              ADV COMPUT MATH                6       159      1996
  2. KNYAZEV AV            SIAM J NUMER ANAL              31     1226      1994
  3. KNYAZEV AV            SOVIET J NUMER ANAL            2       371      1987
  6. Oliveira S
     On the convergence rate of a preconditioned subspace eigensolver
     COMPUTING 63: (3) 219-231 1999
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  7. Diaz AR
     A wavelet-Galerkin scheme for analysis of large-scale problems on simple domains
     INT J NUMER METH ENG 44: (11) 1599-1616 APR 20 1999
     1. BAKHVALOV NS NUMERICAL METHODS AP 221 1994
  8. DeRose GCA, Diaz AR
     Single scale wavelet approximations in layout optimization
     STRUCT OPTIMIZATION 18: (1) 1-11 AUG 1999
     1. BAKHVALOV NS NUMERICAL METHODS AP 221 1994
• 2000:
  1. Andrej Cherkaev
     Variational Methods for Structural Optimization
     Springer (2000) ISBN: 9780387984629
     1. BAKHVALOV NS NUMERICAL METHODS AP 221 1994^M
  2. M. Larin
     An optimal multilevel method for computing the smallest eigenpair
     Bull. Nov. Compt. Center, Num. Anal., 9 (2000), pp. 59-67
     1. KNYAZEV AV ETNS 7 104 1998
     2. DYAKONOV EG RUSSIAN J NUMER ANAL 7 473 1992
  3. DeRose GCA, Diaz AR
     Solving three-dimensional layout optimization problems using fixed scale wavelets
     COMPUT MECH 25: (2-3) 274-285 MAR 2000
     1. BAKHVALOV NS NUMERICAL METHODS AP 221 1994
  4. Ovtchinnikov EE, Xanthis LS
     Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions
     P NATL ACAD SCI USA 97: (3) 967-971 FEB 1 2000
     1. KNYAZEV AV ETNS 7 104 1998
     2. KNYAZEV AV INT SER NUMER MATH O 96 143 1990
  5. Lui SH
     Domain decomposition methods for eigenvalue problems
     JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 117: (1) 17-34 MAY 1 2000
     1. DYAKONOV EG RUSSIAN J NUMER ANAL 7 473 1992
     2. KNYAZEV AV SIAM J NUMER ANAL 31 1225 1994
     3. KNYAZEV AV SOV J NUMER ANAL MAT 4 283 1989
     4. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
  6. Golub GH, Zhang ZY, Zha HY
     Large sparse symmetric eigenvalue problems with homogeneous linear constraints: the Lanczos process with inner-outer iterations
     LINEAR ALGEBRA AND ITS APPLICATIONS 309: (1-3) 289-306 APR 15 2000
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  7. Dobson DC, Gopalakrishnan J, Pasciak JE
     An efficient method for band structure calculations in 3D photonic crystals
     J COMPUT PHYS 161: (2) 668-679 JUL 1 2000
     
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. KNYAZEV AV 143 U COL DENV CTR C
  8. Beattie C
     Galerkin eigenvector approximations
     MATH COMPUT 69: (232) 1409-1434 OCT 2000
     1. KNYAZEV AV MATH COMPUT 66 985 1997
  9. Fan GX, Liu QH, Senn P, Blanchard SP
     3-D numerical mode-matching (NMM) method for resistivity well-logging tools
     IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 48: (10) 1544-1552 OCT 2000
     1. KNYAZEV AV SIAM J NUMER ANAL 31 1226 1994
  10. Golub GH, van der Vorst HA
      Eigenvalue computation in the 20th century
      J COMPUT APPL MATH 123: (1-2) 35-65 Sp. Iss. SI NOV 1 2000
      1. KNYAZEV A IN PRESS TEMPLATES S 2000
      2. KNYAZEV AV ETNS 7 104 1998
  11. Morgan RB
      Preconditioning eigenvalues and some comparison of solvers
      J COMPUT APPL MATH 123: (1-2) 101-115 Sp. Iss. SI NOV 1 2000
      1. KNYAZEV A IN PRESS TEMPLATES S 2000
  12. Yang DQ
      Finite elements for elliptic problems with wild coefficients
      MATHEMATICS AND COMPUTERS IN SIMULATION
      54: (4-5) 383-395 DEC 15 2000
      1. KNYAZEV AV 132 UCD CCM U COL CT 1998
  13. Chizhonkov EV, Lebedev VI
      On acceleration of the convergence of one iterative method
      RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING 15 (5): 383-395 2000
      1. BAKHALOV NS DOKL AKAD NAUK SSSR 319 13 1991
  14. KA Cliffe, A Spence, SJ Tavener
      The numerical analysis of bifurcation problems with application to fluid mechanics
      Acta Numerica (2000), pp. 39-131 c Cambridge University Press, 2000
      1. KNYAZEV AV ETNS 7 104 1998
• 2001:
  1. Neymeyr K
     A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient
     LINEAR ALGEBRA APPL 322: (1-3) 61-85 JAN 1 2001
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. KNYAZEV AV LINEAR ALGEBRA APPL 154 245 1991
     3. KNYAZEV AV USSR J COMPUT MATH M 28 195 1988
     4. KNYAZEV AV ETNS 7 104 1998
  2. Neymeyr K
     A geometric theory for preconditioned inverse iteration II: Convergence estimates
     LINEAR ALGEBRA APPL 322: (1-3) 87-104 JAN 1 2001
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. KNYAZEV AV ETNS 7 104 1998
  3. Ovtchinnikov EE, Xanthis LS
     Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates
     PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 457: (2006) 441-451 FEB 8 2001
     1. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
     2. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     3. KNYAZEV AV ETNS 7 104 1998
  4. Xu JC
     The method of subspace corrections
     JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 128 (1-2): 335-362, Sp. Iss. SI MAR 1 2001
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  5. Bendtsen C, Nielsen OH, Hansen LB
     Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel
     APPLIED NUMERICAL MATHEMATICS 37 (1-2): 189-199 APR 2001
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  6. Volker Mehrmann, David Watkins
     Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils
     SIAM Journal on Scientific Computing Volume 22, Number 6 pp. 1905-1925, 2001
     1. D'yakunov E Vestnik Moskov. Univ. 2 29 1982
  7. Feng YT
     An integrated Davidson and multigrid solution approach for very large scale symmetric eigenvalue problems
     COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 190 (28): 3543-3563 2001
     1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
  8. Bergamaschi L, Pini G, Sartoretto F
     Parallel preconditioning of a sparse eigensolver
     PARALLEL COMPUTING 27 (7): 963-976 JUN 2001
     1. KNYAZEV AV SIAM J NUMER ANAL 31 1226 1994
  9. Martikainen J, Rossi T, Toivanen J
     Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solvers
     COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING 17 (8): 521-527 AUG 2001
     1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
  10. G. W. Stewart
      Matrix Algorithms Vol II
      Cambridge University Press (2001) ISBN: 9780898715033
      1. KNYAZEV AV MATH COMP 1997
• 2002:
  1. O Axelsson, I Farago, J Karatson
     Sobolev space preconditioning for Newton's method using domain decomposition
     Numer. Linear Algebra Appl. 2002; 9:585-598
     1. KNYAZEV AV MATH COMP To appear
  2. Danny C. Sorensen
     Numerical methods for large eigenvalue problems Acta Numerica (2002), 11: 519-584
     1. KNYAZEV AV SIAM J Sci Comput 2001
  3. M. Larin
     Computation of a few smallest eigenvalues and their eigenvectors for large sparse SPD matrices
     Bull. Nov. Compt. Center, Num. Anal., 11 (2002), pp. 75-86
     1. KNYAZEV AV LINEAR ALGEBRA APPL 358 95 2003
     2. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  4. Y. Notay
     Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem
     Numerical Linear Algebra with Applications Volume 9, Issue 1, 2002. Pages: 21-44
     1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
     2. KNYAZEV AV SIAM J Sci Comput 2001 To appear
  5. Tony F. Chan, Ilya Sharapov
     Subspace correction multi-level methods for elliptic eigenvalue problems
     Numerical Linear Algebra with Applications Volume 9, Issue 1, 2002. Pages: 1-20
     1. KNYAZEV AV SIAM J NUMER ANAL 31 1226 1994
  6. Neymeyr K
     A geometric theory for preconditioned inverse iteration applied to a subspace
     MATHEMATICS OF COMPUTATION 71 (237): 197-216 2002
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. DYAKONOV EG MOSCOW U COMPUT MATH 2 32 1982
     3. DYAKONOV EG RUSSIAN J NUMER ANAL 7 473 1992
     4. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
  7. Hiptmair R, Neymeyr K
     Multilevel method for mixed eigenproblems
     SIAM J SCI COMPUT 23 (6): 2141-2164 MAY 17 2002
     
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. KNYAZEV A IN PRESS ELECT T NUM 2001
     3. KNYAZEV A IN PRESS LINEAR ALGE
     4. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
     5. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
     6. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
  8. Neymeyr K
     A posteriori error estimation for elliptic eigenproblems
     NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 9 (4): 263-279 JUN 2002
     
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. DYAKONOV EG MOSCOW U COMPUT MATH 2 32 1982
     3. DYAKONOV EG RUSSIAN J NUMER ANAL 7 473 1992
     4. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
     5. KNYAZEV AV IN PRESS LINEAR ALGE 2001
  9. Stathopoulos A
     A case for a biorthogonal Jacobi-Davidson method: Restarting and correction equation
     SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 24 (1): 238-259 JUL 9 2002
     
     1. KNYAZEV AV INT SER NUMER MATH 96 143 1991
  10. Golub GH, Ye Q
      An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems
      SIAM JOURNAL ON SCIENTIFIC COMPUTING 24 (1): 312-334 AUG 21 2002
      
      1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
      2. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
      3. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
  11. Bergamaschi L, Putti M
      Numerical comparison of iterative eigensolvers for large sparse symmetric positive definite matrices
      COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 191 (45): 5233-5247 2002
      
      1. KNYAZEV AV SIAM J NUMER ANAL 31 1226 1994
  12. Axelsson O, Farago I, Karatson J
      Sobolev space preconditioning for Newton's method using domain decomposition
      NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 9 (6-7): 585-598 Sp. Iss. SI SEP-NOV 2002
      
      1. KNYAZEV AW IN PRESS MATH COMPUT
  13. Arbenz P
      A comparison of factorization-free eigensolvers with application to cavity resonators
      COMPUTATIONAL SCIENCE-ICCS 2002, PT III, PROCEEDINGS LECTURE NOTES IN COMPUTER SCIENCE 2331: 295-304 2002
      
      1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  14. Benzi M
      Preconditioning techniques for large linear systems: A survey
      JOURNAL OF COMPUTATIONAL PHYSICS 182 (2): 418-477 NOV 1 2002
      
      1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
  15. Z Zhao
      Subspace iteration accelerated by using Chebyshev polynomials.
      Journal of Nanjing University of Aeronautics and Astronautics. 34:22, 197-200, 3/2002
      
      1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
• 2003:
  1. Frank Schmidt, Tilmann Friese, Lin Zschiedrich, and Peter Deuflhard.
     Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design.
     In W. Jäger et al., editor, Mathematics - Key Technology for the Future: Joint Problems between Universities and Industry, pages 270-292. Springer, 2003.
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  2. D Fortin, I Tseveendorj
     Maximum Clique Regularizations
     In P. M. Pardalos, I. Tseveendorj, and R. Enkhbat, Eds., Optimization and Optimal Control, 121-139, World Scientific, 2003.
     1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  3. Notay Y
     Convergence analysis of inexact Rayleigh quotient iteration
     SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 24 (3): 627-644 2003
     
     1. KNYAZEV AV LINEAR ALGEBRA APPL 358 95 2003
     2. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
     3. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
  4. Sleijpen GLG, van den Eshof J, Smit P
     Optimal a priori error bounds for the Rayleigh-Ritz method
     MATH COMPUT 72 (242): 677-684 2003
     
     1. KNYAZEV AV MATH COMPUT 66 985 1997
  5. VandeVondele J, Hutter J
     An efficient orbital transformation method for electronic structure calculations
     J CHEM PHYS 118 (10): 4365-4369 MAR 8 2003
     
     1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  6. Heuveline V
     On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods
     J COMPUT PHYS 184 (1): 321-337 JAN 1 2003
     
     1. KNYAZEV AV 16O U TUB STUTTG 2001
  7. Larin M
     On a multigrid eigensolver for linear elasticity problems
     LECT NOTES COMPUT SC 2542: 182-191 2003
     
     1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
  8. Ovtchinnikov E
     Convergence estimates for the generalized Davidson method for symmetric eigenvalue problems I: The preconditioning aspect
     SIAM J NUMER ANAL 41 (1): 258-271 2003
     
     1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
     2. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
     3. KNYAZEV AV IN PRESS ELECT T NUM
     4. KNYAZEV AV INT SER NUMER MATH 96 143 1991
     5. KNYAZEV AV LINEAR ALGEBRA APPL 358 95 2003
     6. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
     7. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
  9. Ovtchinnikov E
     Convergence estimates for the generalized Davidson method for symmetric eigenvalue problems II: The subspace acceleration
     SIAM J NUMER ANAL 41 (1): 272-286 2003
     
     1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
     2. KNYAZEV AV INT SER NUMER MATH 96 143 1991
     3. KNYAZEV AV LINEAR ALGEBRA APPL 358 95 2003
     4. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
     5. KNYAZEV AV SOVIET J NUMER ANAL 2 371 1987
  10. Bergamaschi L, Pini G, Sartoretto F
      Computational experience with sequential and parallel, preconditioned Jacobi-Davidson for large, sparse symmetric matrices
      J COMPUT PHYS 188 (1): 318-331 JUN 10 2003
      
      1. KNYAZEV AV SIAM J NUMER ANAL 31 1226 1994
  11. Mandel J
      Local approximation estimators for algebraic multigrid
      ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 15: 56-65 2003
      
      1. KNYAZEV A IN PRESS SIAM J SCI
  12. Schwetlick H, Schnabel U
      Iterative computation of the smallest singular value and the corresponding singular vectors of a matrix
      LINEAR ALGEBRA AND ITS APPLICATIONS 371: 1-30 SEP 15 2003
      1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  13. Titurus B, Friswell MI, Starek L
      Damage detection using generic elements: Part II. Damage detection
      COMPUTERS & STRUCTURES 81 (24-25): 2287-2299 SEP 2003
      
      1. KNYAZEV AV SIAM J SCI COMPUT 23 2008 2002
  14. Bartsch G, Wulf C
      Adaptive multigrid for Helmholtz problems
      J COMPUT ACOUST 11 (3): 341-350 SEP 2003
      
      1. BRAMBLE JH ADV COMPUT MATH 6 159 1996
  15. A. Nishida.
      A Short Survey of Applications and Evaluations of Preconditioned Conjugate Gradient Method for Large Scale Eigenvalue Problems,
      In Proceedings of the 2003 annual conference of the Japan Society for Industrial and Applied Mathematics, Kyoto University, to appear. (in Japanese).
      
      1. KNYAZEV AV ELECT T NUMER ANAL 7 104 1998
      2. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
      3. A.V.Knyazev and M.E.Argentati Implementation of preconditioned eigensolver using hypre Submitted
  16. D. Fortin and I. Tseveendorj
      Maximum Clique Regularizations
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• 2004
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     Geometric Interpretations of COnjugate Gradient and Related Methods
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     A geometry projection method for shape optimization
     Numer. Meth. Engng 2004; 60:2289-2312.
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     On a multigrid method for solving partial eigenproblems
     Sib. J. Num. Math., 7 (2004), pp.25-42
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  4. A. Nishida.
     Performance Evaluation of Parallel AMG Preconditioned Conjugate Gradient Methods for Large Scale Eigenproblems
     IPSJ SIG Notes, 2004(20), pp.205-210, 2004. (in Japanese)
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     3. A.V.Knyazev and M.E.Argentati Implementation of preconditioned eigensolver using hypre
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     SSI: Overview of Simulation Software Infrastructure for Large Scale Scientific Applications
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     Parallel AMG Preconditioned Conjugate Residual Methods for Nonsymmetric Eigenproblems and its Evalutation
     IPSJ SIG Notes, IPSJ SIG Notes, 2004(81), pp.85-90, 2004. (in Japanese).
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     Eigenvalue Problems as Nonlinear Optimization: Application and Evaluation of Optimization Methodologies
     In Proceedings of the 2004 annual conference of the Japan Society for Industrial and Applied Mathematics, pp.220-221, 2004. (in Japanese).
     1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  8. Zheng WY, Ying LA
     Finite element approximations to the discrete spectrum of the Schrodinger operator with the Coulomb potential
     SIAM JOURNAL ON NUMERICAL ANALYSIS 42 (1): 49-74 2004
     1. KNYAZEV AV LINEAR ALGEBRA APPL 2003 358 95
  9. Dauxois J, Nkiet GM, Romain Y
     Canonical analysis relative to a closed subspace
     LINEAR ALGEBRA AND ITS APPLICATIONS 388: 119-145 SEP 1 2004
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  10. Zhao SJ, Zhang J, Xu YM
      Monitoring of processes with multiple operating modes through multiple principle component analysis models
      INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 43 (22): 7025-7035 OCT 27 2004
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  11. Absil PA, Sepulchre R, Van Dooren P, et al.
      Cubically convergent iterations for invariant subspace computation
      SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 26 (1): 70-96 2004
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  12. Notay Y
      Is Jacobi-Davidson faster than Davidson?
      SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 26 (2): 522-543 2004
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      2. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
  13. Hochstenbach ME
      Harmonic and refined extraction methods for the singular value problem, with applications in least squares problems
      BIT NUMERICAL MATHEMATICS 44 (4): 721-754 DEC 2004
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  14. T Torsti, M Heiskanen, MJ Puska, RM Nieminen
      MIKA: Multigrid-based program package for electronic structure calculations
      Psi_k Newsletter, Highlight of the month, October 2004 No. 65, 105-131
      1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
      2. KNYAZEV AV ETNA 2003
• 2005
  1. Matthew Brand
     Nongrid Embeddings for Dimensionality Reduction
     In Machine Learning: ECML 2005
     by JoГЈo GamaEd. Springer (2005) pp. 47-59. ISBN: 9783540292432
     1. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
  2. JH Bramble, TV Kolev, JE Pasciak
     The approximation of the Maxwell eigenvalue problem using a least-squares method
     Math. Comp,Volume 74, Number 252, Pages 1575-1598, 2005.
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     3. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  3. Michael A. Heroux, Roscoe A. Bartlett, Vicki E. Howle, Robert J. Hoekstra, Jonathan J. Hu, Tamara G. Kolda, Richard B. Lehoucq, Kevin R. Long, Roger P. Pawlowski, Eric T. Phipps, Andrew G. Salinger, Heidi K. Thornquist, Ray S. Tuminaro, James M. Willenbring, Alan Williams, Kendall S. Stanley
     An overview of the Trilinos project
     ACM Transactions on Mathematical Software (TOMS), Volume 31 Issue 3, 397 - 423, 2005.
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     A note on inverse iteration
     NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 12 (1): 1-8 FEB 2005
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     3. KNYAZEV AV RUSSIAN J NUMER ANAL 1987 2 371
  5. Larin M, Il'in V
     Variable-step preconditioned conjugate gradient method for partial symmetric eigenvalue problems
     RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING 20 (2): 161-184 2005
     1. BRAMBLE JH ADV COMPUT MATH 1996 6 159
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     3. KNYAZEV AV ELECTRON T NUMER ANA 2003 15 38
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     5. KNYAZEV AV MATH COMPUT 1997 66 985
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     7. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
  6. Money JH, Ye Q
     Algorithm 845: EIGIFP: A MATLAB program for solving large symmetric generalized eigenvalue problems
     ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 31 (2): 270-279 JUN 2005
     1. KNYAZEV AV ELECT T NUMER ANAL 1998 7 104
     2. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
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  7. Arbenz P, Geus R
     Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
     APPLIED NUMERICAL MATHEMATICS 54 (2): 107-121 JUL 2005
     1. KNYAZEV AV ELECTRON T NUMER ANA 2003 15 38
     2. KNYAZEV AV LINEAR ALGEBRA APPL 2003 358 95
     3. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
  8. Angermann L, Wang S
     Multidimensional exponentially fitted simplicial finite elements for convection-diffusion equations with tensor-valued diffusion
     CALCOLO 42 (2): 71-91 JUL 2005
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     A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods
     INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 64 (2): 204-236 SEP 14 2005
     
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     3. KNYZEV AV ELECTRON T NUMER ANA 2003 7 38
  10. Tomov S, Langou J, Canning A, et al.
      Comparison of Nonlinear conjugate-gradient methods for computing the electronic properties of nanostructure architectures
      LECTURE NOTES IN COMPUTER SCIENCE 3516: 317-325 2005
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  11. T Torsti, V Lindberg, I Makkonen, E Ogando, E. Rasanen, H. Saarikoski, M. J. Puska, R. M. Nieminen
      Real-space electronic-property calculations for nanoscale structures
      HANDBOOK OF THEORETICAL AND COMPUTATIONAL NANOTECHNOLOGY, 2005
      1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
      2. KNYAZEV AV ETNA 2003
  12. P.-A. Absil, C.G. Baker, K.A. Gallivan and A. Sameh
      Adaptive Model Trust Region Methods for Generalized Eigenvalue Problems
      Lecture Notes in Computer Science Volume 3514 / 2005 Chapter: p. 33
      1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  13. Susumu Yamada, Toshiyuki Imamura, Masahiko Machida
      16.447 TFlops and 159-Billion-dimensional Exact-diagonalization for Trapped Fermion-Hubbard Model on the Earth Simulator
      Conference on High Performance Networking and Computing. Proceedings of the 2005 ACM/IEEE conference on Supercomputing 2005 Page: 44
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  14. C Yang
      Solving Large-scale Eigenvalue Problems in SciDAC Applications
      J. Phys.: Conf. Ser. 16 425-434. 2005
      1. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
  15. L. Bergamaschi, A. Martinez, and G. Pini.
      Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems.
      Applied Math. Comput., 2005
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      Generalizations of harmonic and refined Rayleigh-Ritz
      ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 20: 235-252 2005
      1. KNYAZEV AV SOVIET J NUMER ANAL 5 : 265 1990
  17. Qiu L, Zhang YX, Li K
      Unitarily invariant metrics on the Grassmann space
      SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 27 (2): 507-531 2005
      1. KNYAZEV AV Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 2008 2002
  18. Brand M
      Nonrigid embeddings for dimensionality reduction
      LECTURE NOTES IN ARTIFICIAL INTELLIGENCE 3720: 47-59 2005
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
• 2006
  1. Kaledin AL, Kaledin M, Bowman JM
     All-atom calculation of the normal modes of bacteriorhodopsin using a sliding block iterative diagonalization method
     JOURNAL OF CHEMICAL THEORY AND COMPUTATION 2 (1): 166-174 JAN-FEB 2006
     1. KNYAZEV AV ELECT T NUMER ANAL 7 : 104 1998
     2. KNYAZEV AV INT SER NUMER MATH 96 : 143 1991
     3. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  2. A. Borzi and G. Borzi
     Algebraic multigrid methods for solving generalized eigenvalue problems
     International Journal for Numerical Methods in Engineering, 65(8) (2006), 1186-1196.
     1. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
     2. KNYAZEV AV LAA 2003
  3. Stanimire Tomov, Julien Langou, Andrew Canning, Lin-Wang Wang, and Jack Dongarra
     Conjugate-Gradient Eigenvalue Solvers in Computing Electronic Properties of Nanostructure Architectures to appear in Special Issue on Computational Methods and Techniques for Nanoscale Technology Computer Aided Design: The International Journal of Computational Science and Engineering.
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  4. T. Torsti, T. Eirola, J. Enkovaara, T. Hakala, P. Havu, V. Havu, T. Hoyalanmaa, J. Ignatius, M. Lyly, I. Makkonen, T. Rantala, K. Ruotsalainen, E. Rasa¤nen, H. Saarikoski, M. J. Puska,
     Three real-space discretization techniques in electronic structure calculations
     PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS 243 (5): 1016-1053 APR 2006
     1. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
     2. KNYAZEV AV ETNA 2003
  5. Giorgio Pini, Giuseppe Gambolati
     3-D nested eigenanalysis on finite element grids
     Communications in Numerical Methods in Engineering, 2006
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     2. KNYAZEV AV SIAM J SCI COMPUT 23 517 2001
  6. Bergamaschi L, Martinez A, Pini G
     Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems
     APPLIED MATHEMATICS AND COMPUTATION 175 (2): 1694-1715 APR 15 2006
     1. KNYAZEV AV PRECONDITIONED GRADIENT-TYPE ITERATIVE METHODS IN A SUBSPACE FOR PARTIAL GENERALIZED SYMMETRICAL EIGENVALUE PROBLEMS SIAM JOURNAL ON NUMERICAL ANALYSIS 31 : 1226 1994
  7. Neymeyr K
     A geometric theory for preconditioned inverse iteration IV: On the fastest convergence cases
     LINEAR ALGEBRA AND ITS APPLICATIONS 415 (1): 114-139 MAY 1 2006
     
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     6. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
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     Cluster robustness of preconditioned gradient subspace iteration elgensolvers
     LINEAR ALGEBRA AND ITS APPLICATIONS 415 (1): 140-166 MAY 1 2006
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     5. KNYAZEV AV INT SER NUMER MATH 96 : 143 1991
     6. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
     7. KNYAZEV AV MATH NOTES 38 : 998 1986
     8. KNYAZEV AV PRECONDITIONED GRADIENT-TYPE ITERATIVE METHODS IN A SUBSPACE FOR PARTIAL GENERALIZED SYMMETRICAL EIGENVALUE PROBLEMS SIAM JOURNAL ON NUMERICAL ANALYSIS 31 : 1226 1994
     9. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
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     Cluster robust error estimates for the Rayleigh-Ritz approximation I: Estimates for invariant subspaces
     LINEAR ALGEBRA AND ITS APPLICATIONS 415 (1): 167-187 MAY 1 2006
     1. KNYAZEV AV New estimates for Ritz vectors MATHEMATICS OF COMPUTATION 66 : 985 1997
     2. KNYAZEV AV MATH NOTES 38 : 998 1986
     3. KNYAZEV AV SOVIET J NUMER ANAL 2 : 371 1987
  10. Ovtchinnikov E
      Cluster robust error estimates for the Rayleigh-Ritz approximation II: Estimates for eigenvalues
      LINEAR ALGEBRA AND ITS APPLICATIONS 415 (1): 188-209 MAY 1 2006
      
      1. KNYAZEV AV New estimates for Ritz vectors MATHEMATICS OF COMPUTATION 66 : 985 1997
      2. KNYAZEV AV MATH NOTES 38 : 998 1986
      3. KNYAZEV AV SOVIET J NUMER ANAL 2 : 371 1987
      4. KNYAZEV AV UNPUB NEW PRIORI FEM
  11. Solov'ev SI
      Preconditioned iterative methods for a class of nonlinear eigenvalue problems
      LINEAR ALGEBRA AND ITS APPLICATIONS 415 (1): 210-229 MAY 1 2006
      1. KNYAZEV AV ELECT T NUMER ANAL 7 : 104 1998
      2. KNYAZEV AV INT SER NUMER MATH 96 : 143 1991
      3. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
      4. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
      5. KNYAZEV AV TEMPLATES SOLUTION A : 352 2000
  12. Absil PA, Baker CG, Gallivan KA
      A truncated-CG style method for symmetric generalized eigenvalue problems
      JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 189 (1-2): 274-285 MAY 1 2006
      1. KNYAZEV AV LINEAR ALGEBRA APPL 358 : 95 2004
  13. Borzi G
      Computation of cavity resonances by means of adaptive eigenvalues displacement
      AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 60 (3): 244-247 2006
      1. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
  14. Ovtchinnikov EE
      Sharp convergence estimates for the preconditioned steepest descent method for Hermitian eigenvalue problems
      SIAM JOURNAL ON NUMERICAL ANALYSIS 43 (6): 2668-2689 2006
      1. BRAMBLE JH A subspace preconditioning algorithm for eigenvector/eigenvalue computation ADVANCES IN COMPUTATIONAL MATHEMATICS 6 : 159 1996
      2. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
      3. KNYAZEV AV SOVIET J NUMER ANAL 2 : 371 1987
  15. Zhao SJ, Zhang J, Xu YM
      Performance monitoring of processes with multiple operating modes through multiple PLS models
      JOURNAL OF PROCESS CONTROL 16 (7): 763-772 AUG 2006
      1. KNYAZEV AV Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 2008 2002
  16. Berns-Muller J, Graham IG, Spence A
      Inexact inverse iteration for symmetric matrices
      LINEAR ALGEBRA AND ITS APPLICATIONS 416 (2-3): 389-413 JUL 15 2006
      1. KNYAZEV AV ELECT T NUMER ANAL 7 : 104 1998
      2. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
      3. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
  17. Baker CG, Absil PA, Gallivan KA
      An implicit Riemannian Trust-Region method for the symmetric generalized eigenproblem
      LECTURE NOTES IN COMPUTER SCIENCE 3991: 210-217 2006
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  18. Patrikainen A, Meila M
      Comparing subspace clusterings
      IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 18 (7): 902-916 JUL 2006
      1. M.E. Argentati, Principal Angles between Subspaces, http://www-math.cudenver.edu/~aknyazev/teaching/rico/talk_defense.pdf, 2006.
  19. Stathopoulos A
      Using the PRIMME eigensolver in materials science applications
      PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS 243 (9): 2198-2208 JUL 2006
      1. KNYAZEV A BLOPEX http://www-math.cudenver.edu/~aknyazev/software/BLOPEX/
      2. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  20. Galantai A, Hegedus CJ
      Jordan's principal angles in complex vector spaces
      NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 13 (7): 589-598 SEP 2006
      1. KNYAZEV AV Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 2008 2002
  21. Yang C, Meza JC, Wang LW
      A constrained optimization algorithm for total energy minimization in electronic structure calculations
      JOURNAL OF COMPUTATIONAL PHYSICS 217 (2): 709-721 SEP 20 2006
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  22. Kim CW
      A preconditioned iterative method for modal frequency-response analysis of structures with non-proportional damping
      JOURNAL OF SOUND AND VIBRATION 297 (3-5): 1097-1103 NOV 6 2006
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  23. Berns-Muller J, Spence A
      Inexact inverse iteration with variable shift for nonsymmetric generalized eigenvalue problems
      SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 28 (4): 1069-1082 2006
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  24. Chen B, Gao B, Liu TY, et al.
      Fast spectral clustering of data using sequential matrix compression
      LECTURE NOTES IN COMPUTER SCIENCE 4212: 590-597 2006
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  25. Szyld DB
      The many proofs of an identity on the norm of oblique projections
      NUMERICAL ALGORITHMS 42 (3-4): 309-323 JUL 2006
      1. JUJUNASHVILI A THESIS U COLORADO DE : 2005
      2. KNYAZEV AV Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 2008 2002
  26. Hetmaniuk U, Lehoucq R
      Basis selection in LOBPCG
      JOURNAL OF COMPUTATIONAL PHYSICS 218 (1): 324-332 OCT 10 2006
      1. KNYAZEV A 220 UCDCCM : 2005
      2. KNYAZEV AV Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 15 : 38 2003
      3. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
      4. LASHUK I P 16 DOM DEC C : 2005
  27. Susumu Yamada , Toshiyuki Imamura , Takuma Kano , Masahiko Machida,
      Gordon Bell finalists I---High-performance computing for exact numerical approaches to quantum many-body problems on the earth simulator,
      Proceedings of the 2006 ACM/IEEE conference on Supercomputing, November 11-17, 2006, Tampa, Florida
      1. A. V. Knyazev, Preconditioned eigensolvers - An oxymoron?, Electronic Transactions on Numerical analysis, Vol. 7, 104--123, 1998.
      2. Andrew V. Knyazev, Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method, SIAM Journal on Scientific Computing, v.23 n.2, p.517-541, 2001
  28. McCombs JR, Stathopoulos A
      Iterative validation of eigensolvers: A scheme for improving the reliability of Hermitian eigenvalue solvers
      SIAM JOURNAL ON SCIENTIFIC COMPUTING 28 (6): 2337-2358 2006
      1. Andrew V. Knyazev, Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method, SIAM Journal on Scientific Computing, v.23 n.2, p.517-541, 2001
  29. Zhou Y, Saad Y
      A Chebyshev - Davidson algorithm for large symmetric eigenproblems
      SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 29 (3): 954-971 2006
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• 2007
  1. Imtiaz SA, Choudhury MAAS, Shah SL
     Building multivariate models from compressed data
     INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 46 (2): 481-491 JAN 17 2007
     1. KNYAZEV AV Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 2008 2002
  2. Mandel J, Sousedik B
     Adaptive selection of face coarse degrees of freedom in the BDDC and the FETI-DP iterative substructuring methods
     COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 196 (8): 1389-1399 2007
     1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  3. FRISWELL MI amage identification using inverse methods PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 365 (1851): 393-410 FEB 15 2007
     1. KNYAZEV AV Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 2008 2002
  4. Freitag MA, Spence A
     Convergence of inexact inverse iteration with application to preconditioned iterative solves
     BIT NUMERICAL MATHEMATICS 47 (1): 27-44 MAR 2007
     1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  5. Stathopoulos A
     Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part I: Seeking one eigenvalue
     SIAM JOURNAL ON SCIENTIFIC COMPUTING 29 (2): 481-514 2007
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     5. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
     6. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
  6. Vomel C, Tomov SZ, Wang LW, et al.
     The use of bulk states to accelerate the band edge state calculation of a semiconductor quantum dot
     JOURNAL OF COMPUTATIONAL PHYSICS 223 (2): 774-782 MAY 1 2007
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  7. Ying OY, Zhang JE, Luo SM
     Dynamic data driven application system: Recent development and future perspective
     ECOLOGICAL MODELLING 204 (1-2): 1-8 MAY 24 2007
     1. MANDEL J Towards a dynamic data driven application system for wildfire simulation COMPUTATIONAL SCIENCE - ICCS 2005, PT 2 3515 : 632 2005
  8. Lazarov RD, Lu SA, Pereverzev SV
     On the balancing principle for some problems of Numerical Analysis
     NUMERISCHE MATHEMATIK 106 (4): 659-689 JUN 2007
     1. KNYAZEV A Lavrentiev regularization plus Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients MATHEMATICS OF COMPUTATION 72 : 17 2003
  9. Kloucek P, Sorensen DC, Wightman JL
     The approximation and computation of a basis of the trace space H-1/2
     JOURNAL OF SCIENTIFIC COMPUTING 32 (1): 73-108 JUL 2007
     1. KNYAZEV A Lavrentiev regularization plus Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients MATH COMP : 2003
  10. Voss H
      A new justification of the Jacobi-Davidson method for large eigenproblems
      LINEAR ALGEBRA AND ITS APPLICATIONS 424 (2-3): 448-455 JUL 15 2007
      1. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003
  11. Griebel M, Hamaekers J
      Sparse grids for the Schrodinger equation
      ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 41 (2): 215-247 MAR-APR 2007
      1. KNYAZEV AV Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 15 : 38 2003
  12. Bottin F, Zerah G
      Formation enthalpies of monovacancies in aluminum and gold under the condition of intense laser irradiation
      PHYSICAL REVIEW B 75 (17): Art. No. 174114 MAY 2007
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  13. Yang C, Meza JC, Wang LW
      A trust region direct constrained minimization algorithm for the Kohn-Sham equation
      SIAM JOURNAL ON SCIENTIFIC COMPUTING 29 (5): 1854-1875 2007
      1. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  14. Stathopoulos A, McCombs JR
      Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part II: Seeking many eigenvalues
      SIAM JOURNAL ON SCIENTIFIC COMPUTING 29 (5): 2162-2188 2007
      1. KNYAZEV AV BLOPEX
      2. KNYAZEV AV ELECTRON T NUMER ANA 7 : 104 1998
      3. KNYAZEV AV INT SER NUMER MATH 96 : 143 1991
      4. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  15. Bollhofer M, Notay Y
      JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices
      COMPUTER PHYSICS COMMUNICATIONS 177 (12): 951-964 DEC 15 2007
      1. KNYAZEV A BLOPEX BLOCK LOCALLY
      2. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
  16. Toshiyuki Imamura, Susumu Yamada, and Masahiko Machida
      Over 10 TFLOPS Computation for a Huge Sparse Eigensolver on the Earth Simulator
      High Performance Computing on Vector Systems, Springer Berlin Heidelberg, 2007 ISBN: 9783540291244, pp. 51-61.
      1. KNYAZEV AV ETNA 1998
      2. KNYAZEV AV SIAM J SCI COMPUT 2001 23 517
  17. Bollhofer M, Notay Y
      JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices
      COMPUTER PHYSICS COMMUNICATIONS Volume: 177 Issue: 12 Pages: 951-964 Published: DEC 15 2007
      1. KNYAZEV A BLOPEX BLOCK LOCALLY :
      2. KNYAZEV AV Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM JOURNAL ON SCIENTIFIC COMPUTING 23 : 517 2001
• 2008
  1. Gao XB, Golub GH, Liao LZ
     Continuous methods for symmetric generalized eigenvalue problems
     LINEAR ALGEBRA AND ITS APPLICATIONS Volume: 428 Issue: 2-3 Pages: 676-696 Published: JAN 15 2008
     1. KNYAZEV AV A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems LINEAR ALGEBRA AND ITS APPLICATIONS 358 : 95 2003