Anne Greenbaum

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All published works

Action	Title	Year	Authors
+ PDF Chat	When is the Resolvent Like a Rank One Matrix?	2025	Anne Greenbaum Faranges Kyanfar Abbas Salemi
+	Numerical bounds on the Crouzeix ratio for a class of matrices	2024	Michel Crouzeix Anne Greenbaum Kenan Li
+	Comparison of K-spectral set bounds on norms of functions of a matrix or operator	2024	Anne Greenbaum Natalie Wellen
+ PDF Chat	GMRES, pseudospectra, and Crouzeix’s conjecture for shifted and scaled Ginibre matrices	2024	Tyler Chen Anne Greenbaum Thomas Trogdon
+ PDF Chat	Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation	2023	Tyler Chen Anne Greenbaum Cameron Musco Christopher Musco
+	Open Problems in the Analysis of Krylov Subspace Methods	2023	Anne Greenbaum
+	K-Spectral Sets	2023	Anne Greenbaum Natalie Wellen
+	GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices	2023	Tyler Chen Anne Greenbaum Thomas Trogdon
+	Near-Optimal Approximation of Matrix Functions by the Lanczos Method	2023	Noah Amsel Tyler Chen Anne Greenbaum Cameron Musco Chris Musco
+	Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm	2023	Tyler Chen Anne Greenbaum Natalie Wellen
+ PDF Chat	Error Bounds for Lanczos-Based Matrix Function Approximation	2022	Tyler Chen Anne Greenbaum Cameron Musco Christopher Musco
+	Low-memory Krylov subspace methods for optimal rational matrix function approximation	2022	Tyler Chen Anne Greenbaum Cameron Musco Christopher Musco
+ PDF Chat	On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic	2021	Anne Greenbaum Hexuan Liu Tyler Chen
+ PDF Chat	Crouzeix’s Conjecture and Related Problems	2020	Kelly Bickel Pamela Gorkin Anne Greenbaum Thomas Ransford Felix L. Schwenninger Elías Wegert
+ PDF Chat	First-Order Perturbation Theory for Eigenvalues and Eigenvectors	2020	Anne Greenbaum Ren‐Cang Li Michael L. Overton
+	First-order Perturbation Theory for Eigenvalues and Eigenvectors	2019	Anne Greenbaum Ren‐Cang Li Michael L. Overton
+ PDF Chat	Spectral Sets: Numerical Range and Beyond	2019	Michel Crouzeix Anne Greenbaum
+	First-order Perturbation Theory for Eigenvalues and Eigenvectors	2019	Anne Greenbaum Ren‐Cang Li Michael L. Overton
+	On the convergence rate of DGMRES	2018	Anne Greenbaum Faranges Kyanfar Abbas Salemi
+	Spectral Sets: Numerical Range and Beyond	2018	Michel Crouzeix Anne Greenbaum
+ PDF Chat	Some Extensions of the Crouzeix--Palencia Result	2018	Trevor Caldwell Anne Greenbaum Kenan Li
+	Spectral Sets: Numerical Range and Beyond	2018	Michel Crouzeix Anne Greenbaum
+ PDF Chat	Numerical investigation of Crouzeix's conjecture	2017	Anne Greenbaum Michael L. Overton
+	Some Extensions of the Crouzeix-Palencia Result	2017	Trevor Caldwell Anne Greenbaum Kenan Li
+	Variational analysis of the Crouzeix ratio	2016	Anne Greenbaum Adrian S. Lewis Michael L. Overton
+	New Directions in Numerical Computation	2016	Tobin A. Driscoll Alex Townsend Jean‐Paul Berrut Bengt Fornberg Anne Greenbaum Nicholas J. Higham Randy LeVeque Ian H. Sloan
+	Near Normal Dilations of Nonnormal Matrices and Linear Operators	2016	Anne Greenbaum Trevor Caldwell Kenan Li
+ PDF Chat	Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem	2015	Meng‐Huo Chen Anne Greenbaum
+	Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture	2015	Daeshik Choi Anne Greenbaum
+	Iterative Solution Methods for Linear Systems	2013	Anne Greenbaum
+	Crouzeix’s conjecture and perturbed Jordan blocks	2011	Anne Greenbaum Daeshik Choi
+	Matrices That Generate the Same Krylov Residual Spaces	2011	Anne Greenbaum Zdeněk Strakoš
+	Global error bounds for the Petrov-Galerkin discretization of the neutron transport equation	2010	Britton Chang Anne Greenbaum Eric Machorro
+	Upper and lower bounds on norms of functions of matrices	2008	Anne Greenbaum
+	Iterative Solution Methods for Linear Systems	2006	Anne Greenbaum
+	Characterizations of the polynomial numerical hull of degree k	2006	James V. Burke Anne Greenbaum
+	Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport Equation	2005	Baisong Chang Peter N. Brown Anne Greenbaum E M Machorro
+	The polynomial numerical hulls of Jordan blocks and related matrices	2003	Vance Faber Anne Greenbaum Donald E. Marshall
+	Card Shuffling and the Polynomial Numerical Hull of Degree k	2003	Anne Greenbaum
+	Generalizations of the field of values useful in the study of polynomial functions of a matrix	2002	Anne Greenbaum
+ PDF Chat	Estimating the Attainable Accuracy of Recursively Computed Residual Methods	1997	Anne Greenbaum
+	Iterative Methods for Solving Linear Systems	1997	Anne Greenbaum
+	Any Nonincreasing Convergence Curve is Possible for GMRES	1996	Anne Greenbaum Vlastimil Pták Zdeněk Strakoš
+	Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems	1996	Jane Cullum Anne Greenbaum
+	A Further Note on Max-Min Properties of Matrix Factor Norms	1995	Leonid Gurvits Anne Greenbaum
+ PDF Chat	Max-Min Properties of Matrix Factor Norms	1994	Anne Greenbaum Leonid Gurvits
+ PDF Chat	GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems	1994	Anne Greenbaum Lloyd N. Trefethen
+ PDF Chat	Matrices that Generate the same Krylov Residual Spaces	1994	Anne Greenbaum Zdeněk Strakoš
+	Do the Pseudospectra of a Matrix Determine its Behavior	1993	Anne Greenbaum Lloyd N. Trefethen
+	On the numerical solution of the biharmonic equation in the plane	1992	Anne Greenbaum Leslie Greengard Anita Mayo
+ PDF Chat	Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators	1992	Anne Greenbaum
+	Open questions in the convergence analysis of the lanczos process for the real symmetric eigenvalue problem	1992	Zdeněk Strakoš Anne Greenbaum
+	Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations	1992	Anne Greenbaum Zdeněk Strakoš
+	Laplace's equation and the Dirichlet-Neumann map in multiply connected domains	1991	Anne Greenbaum Leslie Greengard G. B. McFadden
+	A Parallel Iterative Method for Solving 3-D Elliptic Partial Differential Equations	1990	Anne Greenbaum Edna Reiter Garry Rodrigue
+	Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences	1989	Anne Greenbaum
+	Analysis of a Multigrid Method as an Iterative Technique for Solving Linear Systems	1984	Anne Greenbaum
+	Convergence properties of the conjugate gradient algorithm in exact and finite precision arithmetic	1981	Anne Greenbaum
+ PDF Chat	Livermore timesharing system. Part 4: library files. Chapter 307: mathematics and statistics software library catalog	1979	R. G. Basinger Anne Greenbaum M Jepson
+	Approximating the inverse of a matrix for use in iterative algorithms on vector processors	1979	P.F. Dubois Anne Greenbaum Garry Rodrigue
+ PDF Chat	Incomplete Cholesky conjugate gradient method for the STAR (5-point operator)	1977	Anne Greenbaum Garry Rodrigue
+ PDF Chat	Livermore Time-Sharing System. Part 4: library files. Chapter 307: Numerical Mathematics Group, Mathematical Software Library Catalog	1977	F. E. Fritsch Anne Greenbaum

Common Coauthors

Coauthor	Papers Together
Tyler Chen	8
Zdeněk Strakoš	5
Michael L. Overton	5
Michel Crouzeix	4
Kenan Li	4
Cameron Musco	4
Garry Rodrigue	3
Ren‐Cang Li	3
Trevor Caldwell	3
Natalie Wellen	3
Christopher Musco	3
Abbas Salemi	2
Leslie Greengard	2
Leonid Gurvits	2
Thomas Trogdon	2
Faranges Kyanfar	2
Daeshik Choi	2
Lloyd N. Trefethen	2
Eric Machorro	1
Tobin A. Driscoll	1
E M Machorro	1
Chris Musco	1
Nicholas J. Higham	1
Ian H. Sloan	1
Adrian S. Lewis	1
Randy LeVeque	1
M Jepson	1
James V. Burke	1
Meng‐Huo Chen	1
Hexuan Liu	1
Peter N. Brown	1
Anita Mayo	1
Britton Chang	1
P.F. Dubois	1
Pamela Gorkin	1
Alex Townsend	1
Felix L. Schwenninger	1
Elías Wegert	1
Donald E. Marshall	1
Edna Reiter	1
R. G. Basinger	1
Vlastimil Pták	1
Bengt Fornberg	1
Kelly Bickel	1
Thomas Ransford	1
Vance Faber	1
G. B. McFadden	1
Noah Amsel	1
Jean–Paul Berrut	1
Jane Cullum	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Bounds for Analytical Functions of Matrices	2004	Michel Crouzeix	12
+	Numerical range and functional calculus in Hilbert space	2006	Michel Crouzeix	10
+	Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences	1989	Anne Greenbaum	8
+ PDF Chat	GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems	1986	Yousef Saad Martin H. Schultz	8
+	Constants related to operators of class C?	1975	Kazuyoshi Ōkubo Tsuyoshi Andô	8
+	Methods of conjugate gradients for solving linear systems	1952	Magnus R. Hestenes Eduard Stiefel	7
+	The Numerical Range is a $(1+\sqrt{2})$-Spectral Set	2017	Michel Crouzeix C. Palencia	7
+ PDF Chat	GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems	1994	Anne Greenbaum Lloyd N. Trefethen	7
+	Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix	1976	Christopher C. Paige	6
+	A proof of Crouzeix’s conjecture for a class of matrices	2013	Daeshik Choi	6
+	Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture	2015	Daeshik Choi Anne Greenbaum	5
+	Hessenberg matrices in krylov subspaces and the computation of the spectrum	1995	Olavi Nevanlinna	5
+ PDF Chat	Max-Min Properties of Matrix Factor Norms	1994	Anne Greenbaum Leonid Gurvits	5
+	Generalizations of the field of values useful in the study of polynomial functions of a matrix	2002	Anne Greenbaum	5
+ PDF Chat	The principle of minimized iterations in the solution of the matrix eigenvalue problem	1951	Walter E. Arnoldi	5
+	Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet	1950	Johann von Neumann	4
+	Iterative Methods for Solving Linear Systems	1997	Anne Greenbaum	4
+ PDF Chat	Some Extensions of the Crouzeix--Palencia Result	2018	Trevor Caldwell Anne Greenbaum Kenan Li	4
+	Conjugate gradient methods for indefinite systems	1976	R. Fletcher	4
+ PDF Chat	QMR: a quasi-minimal residual method for non-Hermitian linear systems	1991	Roland W. Freund No�l M. Nachtigal	4
+	Fields of values and iterative methods	1993	Michael Eiermann	4
+	Crouzeix’s conjecture and perturbed Jordan blocks	2011	Anne Greenbaum Daeshik Choi	4
+	The Symmetric Eigenvalue Problem	1998	Beresford Ν. Parlett	4
+	Variational Iterative Methods for Nonsymmetric Systems of Linear Equations	1983	Stanley C. Eisenstat Howard C. Elman Martin H. Schultz	4
+	An iteration method for the solution of the eigenvalue problem of linear differential and integral operators	1950	Cornelius Lanczos	4
+	Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations	1992	Anne Greenbaum Zdeněk Strakoš	4
+ PDF Chat	An Efficient Algorithm for Computing the Generalized Null Space Decomposition	2015	Nicola Guglielmi Michael L. Overton G. W. Stewart	4
+	Approximation theory and numerical linear algebra	1990	Lloyd N. Trefethen	3
+	Iterative Methods for Solving Linear Systems	2006	Alfio Quarteroni Riccardo Sacco Fausto Saleri	3
+	Finite Blaschke product interpolation on the closed unit disc	2002	Christer Glader Mikael Lindström	3
+	Uniform approximations to functions of a complex variable	1954	S. N. Mergelyan	3
+ PDF Chat	Perturbation Theory for Linear Operators	1995	Tosio Kato	3
+	On error estimation in the conjugate gradient method and why it works in finite precision computations.	2002	Zdeněk Strakoš Petr Tichý	3
+	Numerical Determination of the Field of Values of a General Complex Matrix	1978	Charles R. Johnson	3
+ PDF Chat	Stability of the Lanczos Method for Matrix Function Approximation	2018	Cameron Musco Christopher Musco Aaron Sidford	3
+ PDF Chat	Remarks on the Crouzeix--Palencia Proof that the Numerical Range is a (1+\sqrt2)-Spectral Set	2018	Thomas Ransford Felix L. Schwenninger	3
+	Two polynomial methods of calculating functions of symmetric matrices	1989	Vladimir Druskin Leonid Knizhnerman	3
+	Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems	1973	G. W. Stewart	3
+	A Note on Bounded Interpolation in the Unit Disc	1976	J. P. Earl	3
+	Roundoff-error analysis of a new class of conjugate-gradient algorithms	1980	H. Woźniakowski	3
+	Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods	1980	David M. Young Kang C. Jea	3
+	Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems	1996	Jane Cullum Anne Greenbaum	3
+ PDF Chat	A GENERALIZED CONJUGATE GRADIENT METHOD FOR THE NUMERICAL SOLUTION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS	1976	Paul Concus Gene H. Golub Dianne P. O’Leary	3
+	The analytic capacity of sets in problems of approximation theory	1967	A. G. Vitushkin	3
+ PDF Chat	Estimating the Attainable Accuracy of Recursively Computed Residual Methods	1997	Anne Greenbaum	3
+ PDF Chat	Generalization of von Neumann's spectral sets and integral representation of operators	1999	Bernard Delyon F. Delyon	3
+	Perturbation Theory for Analytic Matrix Functions: The Semisimple Case	2003	Peter Lancaster A. S. Markus Fei Zhou	2
+	Polynomial bounds for small matrices	2013	Michel Crouzeix Frank Gilfeather John Holbrook	2
+	Completely Bounded Maps and Operator Algebras	2003	Vern I. Paulsen	2
+	Harmonic Analysis of Operators on Hilbert Space	1970	Béla Szõkefalvi-Nagy Ciprian Foiaş Hari Bercovici László Kérchy	2