Andrew Knyazev's publications reviewed in Zentralblatt MATH
pre990.04428Knyazev, Andrew V.
Preconditioning eigensolvers -- a Oxymoron? (English)
ETNA, Electron. Trans. Numer. Anal. 7, 104-123 (1998). MSC 1991: *65F1565F5065N25
879.65024Bramble, James H.; Pasciak, Joseph E.; Knyazev, Andrew V.
A subspace preconditioning algorithm for eigenvector/eigenvalue computation. (English)
Adv. Comput. Math. 6(1996), No.2, 159-189 (1997). MSC 1991: *65F1565F35, Reviewer: A.L.Andrew
870.65045Knyazev, Andrew V.
New estimates for Ritz vectors. (English)
Math. Comput. 66, No.219, 985-995 (1997). MSC 1991: *65J1047A1047A30
865.73005Bakhvalov, N.S.; Knyazev, A.V.
Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components. (English)
Marchuk, Guri I. (ed.), Numerical methods and applications. Boca Raton, FL: CRC Press. 221-266 (1994). MSC 1991: *73B2773K2035B27, Reviewer: Th.Levy
835.65058Knyazev, A.V.; Sharapov, I.A.
Variational Rayleigh quotient iteration methods for a symmetric eigenvalue problem. (English)
East-West J. Numer. Math. 1, No.2, 121-128 (1993). MSC 1991: *65F15
826.26006Bakhvalov, N.S.; Knyazev, A.V.; Eglit, M.E.
An inequality of Korn type and orthogonal decompositions in spaces of matrices. (English. Russian original)
Russ. Acad. Sci., Dokl., Math. 48, No.1, 127-129 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 331, No.5, 536-537 (1993). MSC 1991: *26D1035Q7273C02, Reviewer: B.Opic
817.65026Bakhvalov, Nikolai S.; Knyazev, Andrew V.
Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients. (English)
Keyes, David E. (ed.) et al., Domain decomposition methods in scientific and engineering computing. Proceedings of the 7th international conference on domain decomposition, October 27-30, 1993, Pennsylvania State University, PA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 180, 157-162 (1994). MSC 1991: *65F1065N3065F35
812.65031Knyazev, Andrew V.; Skorokhodov, Alexander L.
Preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problems. (English)
SIAM J. Numer. Anal. 31, No.4, 1226-1239 (1994). MSC 1991: *65F1565F3565N25, Reviewer: R.H.W.Hoppe
816.65016Knyazev, A.V.
A parallel algorithm of subspace iterations and its implementation on a multiprocessor with ring architecture. (English)
Russ. J. Numer. Anal. Math. Model. 7, No.1, 55-61 (1992). MSC 1991: *65F1565Y0565Y10
816.65017D'yakonov, E.G.; Knyazev, A.V.
On an iterative method for finding lower eigenvalues. (English)
Russ. J. Numer. Anal. Math. Model. 7, No.6, 473-486 (1992). MSC 1991: *65F1565N2565F35
794.65037Knyazev, A.V.; Skorokhodov, A.L.
Iterative methods of gradient type in a subspace for a partial symmetric generalized eigenvalue problem. (English. Russian original)
Russ. Acad. Sci., Dokl., Math. 45, No.2, 474-478 (1992); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 323, No.6, 1020-1023 (1992). MSC 1991: *65F1565N5535J05, Reviewer: E.Kreyszig
785.65098Knyazev, Andrej V.
Iterative solution of PDE with strongly varying coefficients: Algebraic version. (English)
Beauwens, R. (ed.) et al., Iterative methods in linear algebra. Proceedings of the IMACS international symposium, Brussels, Belgium, 2-4 April, 1991. Amsterdam: North-Holland. 85-89 (1992). MSC 1991: *65N2235J25
779.76016Bakhvalov, N.S.; Knyazev, A.V.
An efficient iterative method for solving the Lame equations for almost incompressible media and Stokes' equations. (English. Russian original)
Sov. Math., Dokl. 44, No.1, 4-9 (1992); translation from Dokl. Akad. Nauk SSSR 319, No.1, 13-17 (1991). MSC 1991: *76D0776N1035Q30, Reviewer: V.A.Sava
766.65096Bakhvalov, N.S.; Knyazev, A.V.; Kobel'kov, G.M.
Iterative methods for solving equations with highly varying coefficients. (English)
Fourth international symposium on domain decomposition methods for partial differential equations, Proc. Symp., Moscow/Russ. 1990, 197-205 (1991). MSC 1991: *65N5565F1035J25
753.73009Bakhvalov, N.S.; Knyazev, A.V.
Methods for efficient computation of averaged characteristics of composites of periodic structure of essentially heterogeneous materials. (Russian)
Vychisl. Protsessy Sist. 8, 52-94 (1991). MSC 1991: *73B2773K2035B27, Reviewer: V.Komkov
731.65023Knyazev, A.V.; Skorokhodov, A.L.
On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem. (English)
Linear Algebra Appl. 154-156, 245-257 (1991). MSC 1991: *65F1565F10, Reviewer: H.Hollatz
725.65042Knyazev, A.V.
A preconditioned conjugate gradient method for eigenvalue problems and its implementation in a subspace. (English)
Numerical treatment of eigenvalue problems. Vol. 5, Proc. Workshop, Oberwolfach/Germ. 1990, ISNM 96, 143-154 (1991). MSC 1991: *65F1565F1065N25, Reviewer: U.Langer
816.65015Knyazev, A.V.; Lebedev, V.I.; Skorokhodov, A.L.
The Temple-Lehmann-type methods in iterative algorithms. (English)
Sov. J. Numer. Anal. Math. Model. 5, No.4-5, 265-273 (1990). MSC 1991: *65F15
746.73001Bakhvalov, N.S.; Knyazev, A.V.
Efficient computation of averaged characteristics of composites of a periodic structure of essentially different materials. (English. Russian original)
Sov. Math., Dokl. 42, No.1, 57-62 (1991); translation from Dokl. Akad. Nauk SSSR 313, No.4, 777-781 (1990). MSC 1991: *73B2773K2065N12, Reviewer: G.Geymonat
733.35033Bakhvalov, N.S.; Knyazev, A.V.
A new iterative algorithm for solving problems of the fictitious flow method for elliptic equations. (English. Russian original)
Sov. Math., Dokl. 41, No.3, 481-485 (1990); translation from Dokl. Akad. Nauk SSSR 312, No.4, 783-786 (1990). MSC 1991: *35J2535A2535B30, Reviewer: M.Kopackova
718.65071Bakhvalov, N.S.; Knyazev, A.V.
A new iterative algorithm for solving the fictitious fluxes method problems for elliptic equations. (English)
Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 225-227 (1990). MSC 1991: *65N2235J25, Reviewer: R.Semerdjieva
825.65025Knyazev, A.V.; Skorokhodov, A.L.
Preconditioned iterative methods in subspace for solving linear systems with indefinite coefficient matrices and eigenvalue problems. (English)
Sov. J. Numer. Anal. Math. Model. 4, No.4, 283-310 (1989). MSC 1991: *65F1065F1565F35
711.65029Knyazev, A.V.; Skorokhodov, A.L.
Modified iterative methods in a subspace for solving systems of the equations with matrices without fixed sign and spectral problems. (Modifitsirovannye iteratsionnye metody v podprostranstve dlya resheniya sistem uravnenij so znakoneopredelennymi matritsami i spektral'nykh zadach). (Russian)
Preprint, Otdel Vychislitel'noj Matematiki AN SSSR, 205. Moskva: Otdel Vychislitel'noj Matematiki AN SSSR. 48 p. R. 0.20 (1988). MSC 1991: *65F1565F1065M06, Reviewer: K.Moszynski
706.65033Knyazev, A.V.; Lebedev, V.I.; Skorokhodov, A.L.
Temple-Lehmann methods in iterative algorithms. (Metody Templya-Limanna v iteratsionnykh algoritmakh). (Russian)
Preprint, Otdel Vychislitel'noj Matematiki AN SSSR, 181. Moskva: Otdel Vychislitel'noj Matematiki AN SSSR. 16 p. R. 0.05 (1988). MSC 1991: *65F15, Reviewer: V.V.B.Burjan
825.65034Knyazev, A.V.
Convergence rate estimates for iterative methods for a mesh symmetric eigenvalue problem. (English)
Sov. J. Numer. Anal. Math. Model. 2, No.5, 371-396 (1987). MSC 1991: *65F1565F1065F35
706.65032Knyazev, A.V.
A practical application of Bauer iterations for neutron-physical calculation. (O prakticheskom primenenii iteratsij Bauehra dlya nejtronno-fizicheskogo rascheta). (Russian)
Preprint, Otdel Vychislitel'noj Matematiki AN SSSR, 79. Moskva: Otdel Vychislitel'noj Matematiki AN SSSR. 11 p. R. 0.07 (1984). MSC 1991: *65F1565R2045K05
706.65034Knyazev, A.V.
The parallel algorithm of subspace iterations and its realization on an electronic computer with annular architecture. (Russian)
Numerical methods and mathematical modeling, Collect. Sci. Works, Moskva, 115-123 (1987). MSC 1991: *65F1565Y10
706.65035Knyazev, A.V.
Methods of simultaneous calculation of some eigenvectors. (O metodakh odnovremennogo vychisleniya neskol'kikh sobstvennykh vektorov). (Russian)
Preprint, Institut Atomnoj Ehnergii Im. I. V. Kurchatova, IAEh-3724/16. Moskva: Institut Atomnoj Ehnergii Im. I. V. Kurchatova. 20 p. R. 0.20 (1983). MSC 1991: *65F15
706.65036Knyazev, A.V.
Some two-step methods for the determination of boundaries of the spectrum of a linear matrix pencil. (O nekotorykh dvukhstupenchatykh metodakh nakhozhdeniya granits spektra linejnogo puchka matrits). (Russian)
Preprint, Institut Atomnoj Ehnergii Im I. V. Kurchatova, IAEh-3749/16. Moskva: Institut Atomnoj Ehnergii Im. I. V. Kurchatova. 28 p. R. 0.25 (1983). MSC 1991: *65F1515A2215A18
695.65019Knyazev, A.V.; Skorokhodov, A.L.
The rate of convergence of the method of steepest descent in a Euclidean norm. (English. Russian original)
U.S.S.R. Comput. Math. Math. Phys. 28, No.5, 195-196 (1988); translation from Zh. Vychisl. Mat. Mat. Fiz. 28, No.10, 1577-1578 (1988). MSC 1991: *65F10
657.65045Knyazev, A.V.; Skorokhodov, A.L.
On the rate of convergence of the method of steepest descent in Euclidean norm. (English)
Zh. Vychisl. Mat. Mat. Fiz. 28, No.10, 1577-1578 (1988). MSC 1991: *65F10, Reviewer: F.Szidarovszky
647.65021Knyazev, A.V.
Methods for derivation of some estimates in the symmetric eigenvalue problem. (Russian)
Vychisl. Protsessy Sist. 5, No.5, 164-173 (1987). MSC 1991: *65F1565N2535P15, Reviewer: P.Burda
626.65033Knyazev, A.V.
Modified gradient methods for spectral problems. (Russian)
Differ. Uravn. 23, No.4, 715-717 (1987). MSC 1991: *65F15, Reviewer: J.Smid
641.65052Knyazev, A.V.
The Kato-Temple block algorithm for estimation of eigenvalues: substantiation and application. (Russian)
Conjugate equations and perturbation theory in problems of mathematical physics, Collect. sci. Works, Moskva 1985, 127-135 (1985). MSC 1991: *65J1047A1047B25, Reviewer: J.Kolomy
616.65059Knyazev, A.V.
Exact a priori error estimates of inequality type in the Rayleigh-Ritz method for symmetric spectral problems without assumptions of definiteness or compactness. (Russian)
Methods of numerical and applied mathematics, Collect. sci. Works, Moskva 1985, 74-88 (1985). MSC 1991: *65J1065N3047A10
601.65032Knyazev, A.V.
Sharp a priori error estimates of the Rayleigh-Ritz method without assumptions of fixed sign or compactness. (English. Russian original)
Math. Notes 38, 998-1002 (1985); translation from Mat. Zametki 38, No.6, 900-907 (1985). MSC 1991: *65J1047A10, Reviewer: H.Marcinkowska
596.65064Lebedev, V.I.; Bakhvalov, N.S.; Agoshkov, V.I.; Baburin, O.V.; Knyazev, A.V.; Shutyaev, V.P.
Parallel algorithms for the solution of some stationary problems of mathematical physics. (Parallel'nye algoritmy resheniya nekotorykh statsionarnykh zadach matematicheskoj fiziki). (Russian)
Moskva: Otdel Vychislitel'noj Matematiki AN SSSR. 143 p. R. 1.02 (1984). MSC 1991: *65N2265F1065-02, Reviewer: R.Farzan
496.65019D'yakonov, E.G.; Knyazev, A.V.
Group iterative method for finding low-order eigenvalues. (English. Russian original)
Mosc. Univ. Comput. Math. Cybern. 1982, No.2, 34-40 (1982); translation from Vestn. Mosk. Univ., Ser. XV 1982, No.2, 29-34 (1982). MSC 1991: *65F15