Andrew V.  Knyazev
Andrew V. Knyazev
AMS Fellow. SIAM Fellow. Prof. Emeritus CU Denver. IEEE Senior member
Verified email at - Homepage
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Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
AV Knyazev
SIAM journal on scientific computing 23 (2), 517-541, 2001
Principal angles between subspaces in an A-based scalar product: algorithms and perturbation estimates
AV Knyazev, ME Argentati
SIAM Journal on Scientific Computing 23 (6), 2008-2040, 2002
Large-scale ab initio calculations based on three levels of parallelization
F Bottin, S Leroux, A Knyazev, G Zérah
Computational Materials Science 42 (2), 329-336, 2008
Preconditioned eigensolvers—an oxymoron
AV Knyazev
Electron. Trans. Numer. Anal 7, 104-123, 1998
A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems
AV Knyazev, K Neymeyr
Linear Algebra and its Applications 358 (1-3), 95-114, 2003
Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in HYPRE and PETSc
AV Knyazev, ME Argentati, I Lashuk, EE Ovtchinnikov
SIAM Journal on Scientific Computing 29 (5), 2224-2239, 2007
Convergence rate estimates for iterative methods for a mesh symmetrie eigenvalue problem
AV Knyazev
Russian Journal of Numerical Analysis and Mathematical Modelling 2 (5), 371-396, 1987
A subspace preconditioning algorithm for eigenvector/eigenvalue computation
JH Bramble, JE Pasciak, AV Knyazev
Advances in computational mathematics 6 (1), 159-189, 1996
Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method
AV Knyazev, K Neymeyr
Electronic Transactions on Numerical Analysis 15, 38-55, 2003
Steepest descent and conjugate gradient methods with variable preconditioning
AV Knyazev, I Lashuk
SIAM Journal on Matrix Analysis and Applications 29 (4), 1267-1280, 2007
New estimates for Ritz vectors
A Knyazev
Mathematics of computation 66 (219), 985-995, 1997
Principal angles between subspaces and their tangents
P Zhu, AV Knyazev
Journal of Numerical Mathematics 21 (4), 325-340, 2013
New a priori FEM error estimates for eigenvalues
AV Knyazev, JE Osborn
SIAM Journal on Numerical Analysis 43 (6), 2647-2667, 2006
Towards a dynamic data driven application system for wildfire simulation
J Mandel, LS Bennethum, M Chen, JL Coen, CC Douglas, LP Franca, ...
International Conference on Computational Science, 632-639, 2005
A preconditioned conjugate gradient method for eigenvalue problems and its implementation in a subspace
AV Knyazev
International Series of Numerical Mathematics 96, 143-154, 1991
Preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problems
AV Knyazev, AL Skorokhodov
SIAM journal on numerical analysis 31 (4), 1226-1239, 1994
Angles between infinite dimensional subspaces with applications to the Rayleigh–Ritz and alternating projectors methods
A Knyazev, A Jujunashvili, M Argentati
Journal of Functional Analysis 259 (6), 1323-1345, 2010
Rayleigh-Ritz majorization error bounds with applications to FEM
AV Knyazev, ME Argentati
SIAM Journal on Matrix Analysis and Applications 31 (3), 1521-1537, 2010
Majorization for changes in angles between subspaces, Ritz values, and graph Laplacian spectra
AV Knyazev, ME Argentati
SIAM Journal on Matrix Analysis and Applications 29 (1), 15-32, 2006
On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem
AV Knyazev, AL Shorokhodov
Linear algebra and its applications 154, 245-257, 1991
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