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Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method

SIAM journal on scientific computing, 2001-01, Vol.23 (2), p.517-541

KNYAZEV, Andrew V

2001

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Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices

SIAM journal on scientific computing, 2015-01, Vol.37 (5), p.S3-S29

2015

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Absolute Value Preconditioning for Symmetric Indefinite Linear Systems

SIAM journal on scientific computing, 2013-01, Vol.35 (2), p.A696-A718

2013

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Large-scale ab initio calculations based on three levels of parallelization

Computational materials science, 2008-04, Vol.42 (2), p.329-336

2008

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Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell

Foundations of computational mathematics, 2017-06, Vol.17 (3), p.713-727

2017

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Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates

SIAM journal on scientific computing, 2002, Vol.23 (6), p.2008-2040

2002

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STEEPEST DESCENT AND CONJUGATE GRADIENT METHODS WITH VARIABLE PRECONDITIONING

SIAM journal on matrix analysis and applications, 2007-01, Vol.29 (4), p.1267-1280

2007

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RAYLEIGH-RITZ MAJORIZATION ERROR BOUNDS WITH APPLICATIONS TO FEM

SIAM journal on matrix analysis and applications, 2010-01, Vol.31 (3), p.1521-1537

2010

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Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators

SIAM journal on matrix analysis and applications, 2013-01, Vol.34 (1), p.244-256

2013

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New a Priori Fem Error Estimates for Eigenvalues

SIAM journal on numerical analysis, 2006-01, Vol.43 (6), p.2647-2667

2006

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Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers

SIAM journal on matrix analysis and applications, 2009-01, Vol.31 (2), p.621-628

2009

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Observations on degenerate saddle point problems

Computer methods in applied mechanics and engineering, 2007-08, Vol.196 (37), p.3742-3749

Knyazev, Andrew V.

2007

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Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra

SIAM journal on matrix analysis and applications, 2007-01, Vol.29 (1), p.15-32

2007

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Preconditioned steepest descent-like methods for symmetric indefinite systems

Linear algebra and its applications, 2016-12, Vol.511, p.274-295

2016

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Sharp Majorization-Type Cluster Robust Bounds for Block Filters and Eigensolvers

SIAM journal on matrix analysis and applications, 2023-01, Vol.44 (4), p.1852-1878

2023

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Rayleigh--Ritz Majorization Error Bounds of Mixed Type

SIAM journal on matrix analysis and applications, 2017-01, Vol.38 (1), p.30-49

2017

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Accelerated Graph-based Nonlinear Denoising Filters

Procedia computer science, 2016, Vol.80, p.607-616

2016

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Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method

Electronic transactions on numerical analysis, 2003-01, Vol.15, p.38

2003

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Band alignment in quantum wells from automatically tuned DFT+U

Physical chemistry chemical physics : PCCP, 2019-03, Vol.21 (11), p.5966-5973

2019

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Angles between infinite dimensional subspaces with applications to the Rayleigh–Ritz and alternating projectors methods

Journal of functional analysis, 2010-09, Vol.259 (6), p.1323-1345

2010

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New estimates for Ritz vectors

Mathematics of computation, 1997-07, Vol.66 (219), p.985-995

Knyazev, Andrew V.

1997

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Accelerated graph-based spectral polynomial filters

2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP), 2015, p.1-6

2015

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Lavrentiev regularization + Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients

Mathematics of computation, 2003-01, Vol.72 (241), p.17-40

2003

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Nonsymmetric Preconditioning for Conjugate Gradient and Steepest Descent Methods1

Procedia computer science, 2015, Vol.51, p.276-285

2015

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Nonsymmetric Preconditioning for Conjugate Gradient and Steepest Descent Methods 1

Procedia computer science, 2015, Vol.51, p.276-285

2015

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Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method

Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices

Absolute Value Preconditioning for Symmetric Indefinite Linear Systems

Large-scale ab initio calculations based on three levels of parallelization

Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell

Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates

STEEPEST DESCENT AND CONJUGATE GRADIENT METHODS WITH VARIABLE PRECONDITIONING

RAYLEIGH-RITZ MAJORIZATION ERROR BOUNDS WITH APPLICATIONS TO FEM

Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators

New a Priori Fem Error Estimates for Eigenvalues

Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers

Observations on degenerate saddle point problems

Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra

Preconditioned steepest descent-like methods for symmetric indefinite systems

Sharp Majorization-Type Cluster Robust Bounds for Block Filters and Eigensolvers

Rayleigh--Ritz Majorization Error Bounds of Mixed Type

Accelerated Graph-based Nonlinear Denoising Filters

Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method

Band alignment in quantum wells from automatically tuned DFT+U

Angles between infinite dimensional subspaces with applications to the Rayleigh–Ritz and alternating projectors methods

New estimates for Ritz vectors

Accelerated graph-based spectral polynomial filters

Lavrentiev regularization + Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients

Nonsymmetric Preconditioning for Conjugate Gradient and Steepest Descent Methods1

Nonsymmetric Preconditioning for Conjugate Gradient and Steepest Descent Methods 1

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