Department of Mathematical Sciences
University of Colorado Denver
P.O. Box 173364, Campus Box 170, Denver, CO 80217-3364.
Street Address: 1250 14th St. Room 644, Denver CO 80202
Phone: (303) 556-8442. Fax: (303) 556-8550
Email: andrew.knyazev@cudenver.edu
Internet: http://math.cudenver.edu/~aknyazev
Education:
Research Support Record:
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NSF Award DMS 0728941, Analysis of Microarray Gene Expression Data, 2007-2008, $99,973
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NSF Award DNS 0612751, Locally Optimal Preconditioned Eigenvalue Solvers, 2006-2010, Continuing Grant: $79,958+$83,134+$86,450=$249,542.
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NSF Award CNS 0420985, MRI: Collaborative Research: Acquisition of an IBM BlueGene/L Supercomputer. 2004-2007, $ 119,332. The co-PI, joint with the PI Jan Mandel.
- DOE, Sandia Labs Robust deflation analysis for preconditioned eigensolvers for large-scale modal analysis. 2004, $ 49,995
- DOE, Lawrence Livermore National Laboratory, Center for Applied Scientific Computing. 2004-2005. Through FusionNumerics
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NSF Award DMS 0208773, Preconditioned Algorithms for Large Eigenvalue Problems. 2002-2006, $ 157,500
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NSF Award DMS 0209311, Sixth IMACS International Symposium on Iterative Methods in Scientific Computing; March 27-30, 2003, Denver, CO. The PI. Joint with the co-PI Harvey J. Greenberg. 2002-2003, $ 16,555
- DOE, Lawrence Livermore National Laboratory, Center for Applied Scientific Computing. Sixth IMACS International Symposium on Iterative Methods in Scientific Computing; March 27-30, 2003, Denver, CO. $3,000
- NASA Earth Science Enterprise's Atmospheric Chemistry Modeling and Data Analysis Program: Towards interactive three-dimensional chemical data assimilation. Joint with Boris Khattatov (The PI), Jean-Francois Lamarque. 2001-2003, $ 177,127
- DOE, Lawrence Livermore National Laboratory, Center for Applied Scientific Computing. Preconditioned Eigensolvers, 2002, $ 53,604
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NSF Award DMS MRI 0079719, Acquisition of a High-Performance Parallel Computer for Mathematical Sciences and Applications. The PI. Joint with co-PI's: Lynn Bennethum. Stephen Billups, Jan Mandel, Thomas Russell. 2000-2001, $ 100,000
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NSF Award DMS 9501507, Mathematical Sciences: Preconditioned Parallel Methods for Large Symmetric Eigenproblems, 1995-1998, $ 60,000
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NSF Award DMS 9508328, Mathematical Sciences Computing Research Environments. Joint with Tom Russell (the PI), Jan Mandel, Leo Franca, and Chaoqun Liu, 1995, $ 50,000
Employment:
- Department of Mathematics, University of Colorado at Denver: Associate Professor, 1994-present
- Courant Institute of Mathematical Sciences,
New York University: Visiting Researcher, 1992-1994
- Institute of Numerical Mathematics Russian Academy of Sciences: Senior Scientist, 1983-1992
- Moscow Physico-Technical Institute (Moscow Institute of Physics and Technology), FPFE, Assistant Professor, 1985-1991
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Moscow State University, Dept. Mathematics and Mechanics: Instructor, 1986-1988
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Moscow Institute of Engineering and Physics: Instructor, 1982-1985
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Kurchatov's Institute of Atomic Energy, Nuclear Reactors: Software Engineer, 1981-1983
Awards:
- Teaching Excellence Award for the College of Liberal Arts and Sciences at the University of Colorado at Denver, 2000
- Faculty Research Fellowship, University of Colorado at Denver, 2000
- Researcher/Creative Artist Award for the College of Liberal Arts and Sciences at the University of Colorado at Denver, 1999
- CU-Denver nominee for the University of Colorado President's Faculty Excellence Award for Advancing Teaching and Learning through Technology, 1999
Research Interests:
- numerical linear algebra, iterative solution of large sparse linear systems and eigenproblems, bounds for eigenvalues;
- numerical solution of partial differential equations, homogenization, numerical methods in linear elasticity, domain decomposition, embedding and multigrid methods, finite element methods;
- parallel computation, software development;
- electronic structure calculations in nanosciences;
- spectral clustering in data mining and information retrieval, spectral image segmentation and graph partitioning;
- clustering of DNA microarray and tiling array data.
Two books (in Russian) and over 50 papers and reports were published. Selected papers:
- F. Bottin, S. Leroux, A. Knyazev, G. Zerah, Large scale ab initio calculations based on three levels of parallelization. (2007). Computational Material Science
- A. V. Knyazev, Observations on degenerate saddle point problems. Computer Methods in Applied Mechanics and Engineering (2007). 196, Issues 37-40, 3742-3749.
- A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov, Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc (2007). SIAM Journal on Scientific Computing, 25(5): 2224-2239.
- Knyazev, Andrew V.; Argentati, Merico E. Majorization for changes in angles between subspaces, Ritz values, and graph Laplacian spectra. SIAM J. Matrix Anal. Appl. 29 (2006/07), no. 1, 15--32.
- A. V. Knyazev and J. Osborn, New A Priori FEM Error Estimates for Eigenvalues. SIAM Journal on Numerical Analysis (SINUM), 43 (2006), no. 6 2647-2667.
- A. V. Knyazev, Analysis of transmission problems on Lipschitz boundaries in stronger norms. Journal of Numerical Mathematics, 11, no. 3 (2003), 225-234.
- A. Knyazev and K. Neymeyr, A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems. Linear Algebra and Its Applications, 358 (2003), Issues 1-3, 95-114.
- A. V. Knyazev and O. Widlund, Lavrentiev Regularization + Ritz Approximation = Uniform Finite Element Error Estimates for Differential Equations with Rough Coefficients. Mathematics of Computation, 72 (2003), 17-40.
- A. V. Knyazev and M. E. Argentati, Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates. SIAM Journal on Scientific Computing, 23 (2002), no. 6, 2009-2041.
- N. S. Bakhvalov, A. V. Knyazev, and R. R. Parashkevov, Extension Theorems for Stokes and Lame equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients. Numerical Linear Algebra with Applications, 9 (2002) no. 2, 115-139.
- A. V. Knyazev, Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method. SIAM Journal on Scientific Computing 23 (2001), no. 2, pp. 517-541.
- A. V. Knyazev, Preconditioned eigensolvers: practical algorithms. In `Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide,'' Editors: Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, and Henk Van der Vorst, SIAM, (2000) 337-368.
- A. V. Knyazev, Preconditioned eigensolvers - an oxymoron?, Electronic Transactions on Numerical Analysis, 7 (1998), 104-123.
- A.V. Knyazev, New estimates for Ritz vectors. Math. Comp. 66 (1997), no. 219, 985-995.
- J. H. Bramble, J. E. Pasciak, A. V. Knyazev, A subspace preconditioning algorithm for eigenvector/eigenvalue computatio. Advances in Computational Mathematics, 6 (1996), no. 2, 159-189.
- A. V. Knyazev and A. L. Skorokhodov, The preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problem, SIAM J. Numerical Analysis, 31, (1994) 1226-1239.
- N. S. Bakhvalov and A. V. Knyazev, Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components, In Numerical Methods and Applications, Ed. Gury I. Marchuk, CRC Press, 221-276, 1994.
- A. V. Knyazev, A. L. Skorokhodov, On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem. Linear Algebra Appl. 154/156 (1991), 245-257.
- A. V. Knyazev, Iterative solution of PDE with strongly varying coefficients: algebraic version. Iterative methods in linear algebra (Brussels, 1991), 85-89, North-Holland, Amsterdam, 1992.
- A. V. Knyazev, Sharp a priori error estimates for the Rayleigh-Ritz method with no assumptions on fixed sign or compactness. Math. Notes 38 (1985), no. 5-6, 998-1002.
- E. G. D'yakonov, A. V. Knyazev, Group iterative method for finding lower-order eigenvalues. Moscow Univ., Ser. 15, Math. Cyber. (1982), no. 2, 32-40.
- Sixth IMACS International Symposium on Iterative Methods in Scientific Computing, University of Colorado at Denver, March 27-30, 2003 (organizer)
- Householder Symposium XV, June 17th - 21st, 2002, Peebles, Scotland:
Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method (invited)
- Miniworkshop: Preconditioning in Eigenvalue Computations (organizer), 03.03. - 09.03.2002, Oberwolfach.
- Schnelle LпїЅser fпїЅr partielle Differentialgleichungen, 27.05. - 02.06.2001, Oberwolfach:
Uniform Finite Element Error Estimates for Differential Equations with Jumps in the Coefficients (invited) - PRISM'2001, May 21-23, 2001, University of Nijmegen, The Netherlands:
Uniform Finite Element Error Estimates for Differential Equations with Jumps in the Coefficients (invited) -
III International Workshop on Accurate Solution of Eigenvalue Problems, July 3-6, 2000, Hagen, Germany
Eigensolvers based on polynomials of two variables (invited) -
USNCCM'99, August 4-6, 1999, University of Colorado at Boulder
Modern Iterative Solvers for Large Symmetric Eigenvalue Problems,
at the MiniSymposium
Very Large Eigenvalue Problems (organizer)
Domain Decomposition Methods for Eigenproblems,
at the MiniSymposium Domain Decomposition Techniques (invited) - International Symposium on Theory and Algorithms for Large Scale Matrix Problems, Dalian University of Technology, Dalian, China August 2-5, 1998 Preconditioned eigensolvers (invited)
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Iterative solution methods for the elasticity equations as arising in mechanics and biomechanics IMMB'98 September 28-30, 1998, University of Nijmegen, The Netherlands
Iterative solution of the Lame equations with highly discontinuous coefficients (invited) -
SIAM 45th Anniversary Meeting, July 14-18, 1997, Stanford University
Minisymposium Preconditioned Methods for Large Eigenproblems (organizer) - Workshop in pre-conditioning eigenvalue problems, May 14-16, 1997, Argonne
- IMACS Symp. Iterative methods in linear algebra, Brussels, 1991 (invited)
- Eigenwertaufgaben in Natur- und Ingenieurwissenschaften und ihre numerische Behandlung, Oberwolfach, 1990 (invited)
- XI HOUSEHOLDER SYMPOSIUM, Tylosand, SWEDEN, 1990 (invited)
- Undergraduate: Calculus I, II, and III, Applied Linear Algebra, Numerical Analysis I and II, Elementary Differential Equations, Complex Variables.
- Graduate: Applied Linear Algebra, Applied Analysis, Approximation Theory, Numerical Linear Algebra, Iterative Methods, Functional Analysis.
Major Recent Service:
- College of Liberal Arts and Sciences - CU-Denver
- 1999-2001 Center for Computational Mathematics, Director
- Campus-wide - CU-Denver
- 2002-2004 Reappointement Tenure and Promotion Committee
- System-wide - University of Colorado
- 2005-2006 President’s Teaching and Learning Collaborative steering committee
- Outside of University of Colorado
- 2001-2007 Editorial board of Comp. Methods in Applied Math.
- 2006-pres Editorial board of Int. J. Comp. Sci. and Math.
- 2002-2004 NERSC Computational Review Panel
- 2002 Organizer of Oberwolfach Miniworkshop Preconditioning in Eigenvalue Computations
- 2003 Organizer of Sixth IMACS International Symposium on Iterative Methods in Scientific Computing, CU-Denver
- 2003-2005 Guest Editor of Linear Algebra and Its Applications
- 2003-2006 Guest Editor of Applied Numerical Mathematics
- 1998-pres Regular referee and panelist for the NSF program in Numerical Mathematics
- Public software development
