D'yakonov, E. G.; Knyazev, A. V. A group iteration method for finding the lowest eigenvalues. (Russian) Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1982, no. 2, 29--34, 81.
Knyazev, A. V. Sharp a priori error estimates for the Rayleigh-Ritz method with no assumptions on fixed sign or compactness. Math. Notes 38 (1985) 998--1002.
Knyazev, A. V. Computation of eigenvalues and eigenvectors for mesh problems: algorithms and error estimates. Department of Numerical Mathematics, USSR Academy of sciences, Moscow 1986. In Russian.
Knyazev, A. V. Convergence rate estimates for iterative methods for a mesh symmetric eigenvalue problem. Soviet J. Numer. Anal. Math. Modelling 2 (1987), no. 5, 371--396.
Knyazev, A. V.; Skorokhodov, A. L. The rate of convergence of the method of steepest descent in the Euclidean norm. U.S.S.R. Comput. Math. and Math. Phys. 28 (1988), no. 5, 195--196 (1990)
Knyazev, A. V.; Lebedev, V. I.; Skorokhodov, A. L. The Temple-Lehmann-type methods in iterative algorithms. Soviet J. Numer. Anal. Math. Modelling 5 (1990), no. 4-5, 265--273.
N. S. Bakhvalov and A. V. Knyazev, A new iterative algorithm for solving problems of the fictitious flow method for elliptic equations Soviet Math. Doklady, v.41, n.3, 1990, 481--485.
N. S. Bakhvalov and A. V. Knyazev, Efficient computation of averaged characteristics of composites of a periodic structure of essentially different materials Soviet Math. Doklady, v. 42, n. 1, 1991, 57--62.
N.S. Bakhvalov, A.V. Knyazev, G.M. Kobel'kov, Iterative methods for solving equations with highly varying coefficients. Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Moscow, 1990), 197--205, SIAM, Philadelphia, PA, 1991.
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.
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.
N. S. Bakhvalov and A. V. Knyazev, Preconditioned Iterative Methods in a Subspace for Linear Algebraic Equations with Large Jumps in the Coefficients, In Domain Decomposition Methods in Science and Engineering, Eds. D. Keyes and J. Xu, American Mathematical Society, Providence, Contemporary Mathematics, v. 180. 157--162, 1994
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), no. 4, 1226-1239.
N. S. Bakhvalov and A. V. Knyazev, Preconditioned Iterative Methods in a Subspace, In Domain Decomposition Methods in Science and Engineering, Ed. D. Keyes and J. Xu, AMS, 157-162, 1995.
Bramble, James H.; Pasciak, Joseph E.; Knyazev, Andrew V. A subspace preconditioning algorithm for eigenvector/eigenvalue computation. Advances in Computational Mathematics, 6 (1996), no. 2, 159--189.
Knyazev, Andrew V. New estimates for Ritz vectors. Math. Comp. 66 (1997), no. 219, 985--995.
A. V. Knyazev, Preconditioned eigensolvers - an oxymoron?, ETNA, 7 (1998), pp. 104-123.
A. V. Knyazev,
Preconditioned eigensolvers. 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, pp. 337-368, 2000.
An extended revision
``Preconditioned eigensolvers: practical algorithms'', published
as a technical report
UCD-CCM 143, 1999, at the Center for Computational
Mathematics, University of Colorado Denver.
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.
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 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.
A. V. Knyazev and Olof Widlund, Lavrentiev Regularization + Ritz Approximation = Uniform Finite Element Error Estimates for Differential Equations with Rough Coefficients. Mathematics of Computation, 72 (2003), 17-40. Known typos.
Andrew Knyazev and Klaus 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. An extended version, with numerical results, is published as a technical report UCD-CCM 173, 2001, at the Center for Computational Mathematics, University of Colorado Denver.
Andrew Knyazev and Klaus Neymeyr, Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method. ETNA, 15 (2003), 38-55.
A. V. Knyazev Analysis of transmission problems on Lipschitz boundaries in stronger norms. Journal of Numerical Mathematics, 11, no. 3 (2003), 225-234.
Stephen Billups, Andrew Knyazev and Jan Mandel, Introduction, Applied Numerical Mathematics, 54, 2 (2005), pp. 105-106.
Jan Mandel, Lynn S. Bennethum, Mingshi Chen, Janice L. Coen, Craig C. Douglas, Leopoldo P. Franca, Craig J. Johns, Minjeong Kim, Andrew V. Knyazev, Robert Kremens, Vaibhav Kulkarni, Guan Qin, Anthony Vodacek, Jianjia Wu, Wei Zhao, and Adam Zornes, Towards a Dynamic Data Driven Application System for Wildfire Simulationi, in: V.S. Sunderam et al. (Eds.): Computational Science - Proceedings ICCS'2005, Lecture Notes in Computer Science 3515, (2005) pp. 632-639.
A. V. Knyazev and M. E. Argentati, Implementation of a Preconditioned Eigensolver Using Hypre, Technical report UCD-CCM 220, April 2005, at the Center for Computational Mathematics, University of Colorado Denver.
A. V. Knyazev and M. E. Argentati, On Proximity of Rayleigh Quotients for Different Vectors and Ritz Values Generated by Different Trial Subspaces. Linear Algebra and Its Applications, 415 (2006), no. 1, 82-95.
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. An extendent version published as a technical report UCD-CCM 215, 2004, at the Center for Computational Mathematics, University of Colorado Denver. See comments.
A. V. Knyazev and M. E. Argentati, Majorization for Changes in Angles Between Subspaces, Ritz values, and graph Laplacian spectra, SIAM Journal on Matrix Analysis and Applications (SIMAX), 29 (2006), no. 1, pp. 15-32. Published as a technical report UCD-CCM 223, 2005, at the Center for Computational Mathematics, University of Colorado Denver. The updated version is at arXiv.org math.NA/0508591.
I. Lashuk, M. E. Argentati, E. Ovchinnikov and A. V. Knyazev, Preconditioned Eigensolver LOBPCG in hypre and PETSc. In Lecture Notes in Computational Science and Engineering, v. 55 (Proceedings of the 16th International Conference on Domain Decomposition Methods. 2005). Editors: O.~B. Widlund and D.~E. Keyes, pages 635-642. Springer, Berlin, 2007. ISBN: 3-540-34468-3.
A. V. Knyazev, Observations on degenerate saddle point problems. Computer Methods in Applied Mechanics and Engineering (2007). 196, Issues 37-40, 3742-3749. Special Issue Honoring the 80th Birthday of Professor Ivo Babuška Also published as a technical report http://arxiv.org/abs/0704.1066.
F. Bottin, S. Leroux, A. Knyazev, G. Zerah, Large scale ab initio calculations based on three levels of parallelization. (2007). Computational Material Science. In print. Published as a technical report http://arxiv.org/abs/0707.3405.
A. V. Knyazev, I. Lashuk, Steepest descent and conjugate gradient methods with variable preconditioning, SIAM Journal on Matrix Analysis and Applications (SIMAX) 29(4), 1267-1280, (2007). Also technical report arXiv.org math.NA/0605767.
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 (SISC). 25(5): 2224-2239, http://dx.doi.org/10.1137/060661624. Also technical report http://arxiv.org/abs/0705.2626.
M. E. Argentati, A. V. Knyazev, C. C. Paige, and I. Panayotov, Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix, SIAM Journal on Matrix Analysis and Applications (SIMAX), Vol.30, No.2, pp. 548-559, (2008). http://dx.doi.org/10.1137/070684628. Also published as a technical report http://arxiv.org/abs/math/0610498.
A. V. Knyazev and M. E. Argentati, Rayleigh-Ritz majorization error bounds with applications to FEM and subspace iterations, (2007). Submitted to SIMAX. Published as a technical report http://arxiv.org/abs/math/0701784.
A. V. Knyazev, A. Jujunashvili, and M. E. Argentati, Angles Between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods (2007). Submitted to Journal of Functional Analysis. Published as a technical report http://arxiv.org/abs/0705.1023.
A. Knyazev and K. Neymeyr, Gradient flow approach to geometric convergence analysis of preconditioned eigensolvers(2008). Submitted to SIMAX. Published as a technical report http://arxiv.org/abs/0801.3099.