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Open Problems in the Analysis of Krylov Subspace Methods

Notices of the American Mathematical Society, 2023-05, Vol.70 (5), p.1

Greenbaum, Anne

2023

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Comparison of K-spectral set bounds on norms of functions of a matrix or operator

Linear algebra and its applications, 2024-08, Vol.694, p.52-77

2024

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Spectral Sets: Numerical Range and Beyond

SIAM journal on matrix analysis and applications, 2019-01, Vol.40 (3), p.1087-1101

2019

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GMRES, pseudospectra, and Crouzeix’s conjecture for shifted and scaled Ginibre matrices

Mathematics of computation, 2025-01, Vol.94 (351), p.241-261

2025

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Estimating the Attainable Accuracy of Recursively Computed Residual Methods

SIAM journal on matrix analysis and applications, 1997-07, Vol.18 (3), p.535-551

Greenbaum, Anne

1997

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Numerical bounds on the Crouzeix ratio for a class of matrices

Calcolo, 2024-06, Vol.61 (2), Article 32

2024

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Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation

SIAM journal on matrix analysis and applications, 2023-06, Vol.44 (2), p.670-692

2023

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Some Extensions of the Crouzeix--Palencia Result

SIAM journal on matrix analysis and applications, 2018-01, Vol.39 (2), p.769-780

2018

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First-Order Perturbation Theory for Eigenvalues and Eigenvectors

SIAM review, 2020, Vol.62 (2), p.463-482

2020

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Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture

SIAM journal on matrix analysis and applications, 2015-01, Vol.36 (1), p.289-301

2015

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On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic

SIAM journal on scientific computing, 2021-01, Vol.43 (5), p.S496-S515

2021

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Error Bounds for Lanczos-Based Matrix Function Approximation

SIAM journal on matrix analysis and applications, 2022-01, Vol.43 (2), p.787-811

2022

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Numerical investigation of Crouzeix's conjecture

Linear algebra and its applications, 2018-04, Vol.542, p.225-245

2018

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On the convergence rate of DGMRES

Linear algebra and its applications, 2018-09, Vol.552, p.219-238

2018

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Recent Advances in Iterative Methods

1, 1994

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An Algorithm for Finding a 2-Similarity Transformation from a Numerical Contraction to a Contraction

SIAM journal on matrix analysis and applications, 2015-01, Vol.36 (3), p.1248-1262

2015

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Crouzeix’s conjecture and perturbed Jordan blocks

Linear algebra and its applications, 2012-04, Vol.436 (7), p.2342-2352

2012

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Any Nonincreasing Convergence Curve is Possible for GMRES

SIAM journal on matrix analysis and applications, 1996-07, Vol.17 (3), p.465-469

1996

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Upper and lower bounds on norms of functions of matrices

Linear algebra and its applications, 2009, Vol.430 (1), p.52-65

Greenbaum, Anne

2009

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Variational analysis of the Crouzeix ratio

Mathematical programming, 2017-07, Vol.164 (1-2), p.229-243

2017

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Near Normal Dilations of Nonnormal Matrices and Linear Operators

SIAM journal on matrix analysis and applications, 2016-01, Vol.37 (4), p.1365-1381

2016

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Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions

Journal of computational physics, 2007-01, Vol.220 (2), p.900-914

2007

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Crouzeix’s Conjecture and Related Problems

Computational methods and function theory, 2020-11, Vol.20 (3-4), p.701-728

2020

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Generalizations of the field of values useful in the study of polynomial functions of a matrix

Linear algebra and its applications, 2002-05, Vol.347 (1), p.233-249

Greenbaum, Anne

2002

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GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems

SIAM journal on scientific computing, 1994-03, Vol.15 (2), p.359-368

1994

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Open Problems in the Analysis of Krylov Subspace Methods

Comparison of K-spectral set bounds on norms of functions of a matrix or operator

Spectral Sets: Numerical Range and Beyond

GMRES, pseudospectra, and Crouzeix’s conjecture for shifted and scaled Ginibre matrices

Estimating the Attainable Accuracy of Recursively Computed Residual Methods

Numerical bounds on the Crouzeix ratio for a class of matrices

Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation

Some Extensions of the Crouzeix--Palencia Result

First-Order Perturbation Theory for Eigenvalues and Eigenvectors

Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture

On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic

Error Bounds for Lanczos-Based Matrix Function Approximation

Numerical investigation of Crouzeix's conjecture

On the convergence rate of DGMRES

Recent Advances in Iterative Methods

An Algorithm for Finding a 2-Similarity Transformation from a Numerical Contraction to a Contraction

Crouzeix’s conjecture and perturbed Jordan blocks

Any Nonincreasing Convergence Curve is Possible for GMRES

Upper and lower bounds on norms of functions of matrices

Variational analysis of the Crouzeix ratio

Near Normal Dilations of Nonnormal Matrices and Linear Operators

Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions

Crouzeix’s Conjecture and Related Problems

Generalizations of the field of values useful in the study of polynomial functions of a matrix

GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems

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