Superlinear convergence of the rational Arnoldi method for the approximation of matrix functions

DOI10.1007/s00211-011-0434-8zbMath1271.65059OpenAlexW1982786226MaRDI QIDQ431305

Bernhard Beckermann, Stefan Güttel

Publication date: 26 June 2012

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-011-0434-8

zbMATH Keywords

potential theorymatrix square rootKrylov spaceHermitian matrixsuperlinear convergencematrix functionsArnoldi iterationCauchy-Stieltjes transformconvergence of iterative methodsrational Krylov method

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Hermitian, skew-Hermitian, and related matrices (15B57) Iterative numerical methods for linear systems (65F10) Potentials and capacities on other spaces (31C15) Matrix exponential and similar functions of matrices (15A16)

Related Items (13)

A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions ⋮ Acceleration of contour integration techniques by rational Krylov subspace methods ⋮ Limited‐memory polynomial methods for large‐scale matrix functions ⋮ A rational Arnoldi process with applications ⋮ Orthogonal rational functions on the unit circle with prescribed poles not on the unit circle ⋮ Low-Rank Updates of Matrix Functions ⋮ A Comparison of Limited-memory Krylov Methods for Stieltjes Functions of Hermitian Matrices ⋮ Convergence rates for inverse-free rational approximation of matrix functions ⋮ Extended and rational Hessenberg methods for the evaluation of matrix functions ⋮ Krylov subspace methods for functions of fractional differential operators ⋮ Scaled and Squared Subdiagonal Padé Approximation for the Matrix Exponential ⋮ Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection ⋮ Automatic Smoothness Detection of the Resolvent Krylov Subspace Method for the Approximation of $C_0$-Semigroups

Uses Software

• mftoolbox

Cites Work

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