A generalization of the steepest descent method for matrix functions

zbMath1171.65367MaRDI QIDQ836727

Michael Eiermann, Oliver G. Ernst, Martin Afanasjew, Stefan Güttel

Publication date: 8 September 2009

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/130652

zbMATH Keywords

steepest descentasymptotic convergence ratepolynomial interpolationmatrix functionlinear system of equationsKrylov subspace approximationrestarted Arnoldi/Lanczos methodrestarted Krylov subspace method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical linear algebra (65F99)

Related Items (12)

A framework of the harmonic Arnoldi method for evaluating \(\varphi\)-functions with applications to exponential integrators ⋮ On the Forsythe conjecture ⋮ Randomized Sketching for Krylov Approximations of Large-Scale Matrix Functions ⋮ Krylov Subspace Restarting for Matrix Laplace Transforms ⋮ Recursion relations for the extended Krylov subspace method ⋮ Speeding Up Krylov Subspace Methods for Computing \(\boldsymbol{{f}(A){b}}\) via Randomization ⋮ Some observations on weighted GMRES ⋮ Implementation of a restarted Krylov subspace method for the evaluation of matrix functions ⋮ Extended and rational Hessenberg methods for the evaluation of matrix functions ⋮ The extended Krylov subspace method and orthogonal Laurent polynomials ⋮ Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection ⋮ A posteriori error estimates of Krylov subspace approximations to matrix functions

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