Numerical range, GMRES and Faber polynomials.

DOI10.1016/j.crma.2005.04.027zbMath1076.47004OpenAlexW2000623902MaRDI QIDQ556960

Bernhard Beckermann

Publication date: 23 June 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.04.027

zbMATH Keywords

Hilbert spacenumerical rangeGMRESFaber polynomialnon-Hermitian systems of linear equations

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Iterative numerical methods for linear systems (65F10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items (15)

A Kreiss type inequality for rational functions on general domains ⋮ Faber polynomials and spectrum localisation ⋮ Convergence analysis of the extended Krylov subspace method for the Lyapunov equation ⋮ GMRES algorithms over 35 years ⋮ A Comparison of Limited-memory Krylov Methods for Stieltjes Functions of Hermitian Matrices ⋮ Residual and Restarting in Krylov Subspace Evaluation of the $\varphi$ Function ⋮ Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices ⋮ Some uses of the field of values in numerical analysis ⋮ ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations ⋮ On the Stability of Network Indices Defined by Means of Matrix Functions ⋮ Comments on the GMRES Convergence for Preconditioned Systems ⋮ A new investigation of the extended Krylov subspace method for matrix function evaluations ⋮ A GMRES Convergence Analysis for Localized Invariant Subspace Ill-Conditioning ⋮ Convergence analysis of the one-step iterative Krylov subspace methods ⋮ Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture

Uses Software

• Schwarz-Christoffel

Cites Work

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• Convex domains and K-spectral sets
• Fields of values and iterative methods
• Some estimates for analytic functions of strip or sectorial operators
• Operators with numerical range in a parabola
• On Faber polynomials and Faber expansions
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Geometric aspects of the theory of Krylov subspace methods
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
• Spectral Inclusion and Analytic Continuation
• Generalization of von Neumann's spectral sets and integral representation of operators
• The Kreiss Matrix Theorem on a General Complex Domain

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