The rational Arnoldi process is a popular method for the computation of a few eigenvalues of a large non-Hermitian matrix A∈Cn×n and for the approximation of matrix functions. The method is particularly attractive when the rational functions that determine the process have only few distinct poles zj∈C, because then few factorizations of matrices of the form A - zjI have to be computed. We discuss recursion relations for orthogonal bases of rational Krylov subspaces determined by rational functions with few distinct poles. These recursion formulas yield a new implementation of the rational Arnoldi process. Applications of the rational Arnoldi process to the approximation of matrix functions as well as to the computation of eigenvalues and pseudospectra of A are described. The new implementation is compared to several available implementations.

A rational Arnoldi process with applications

RODRIGUEZ, GIUSEPPE;
2016

Abstract

The rational Arnoldi process is a popular method for the computation of a few eigenvalues of a large non-Hermitian matrix A∈Cn×n and for the approximation of matrix functions. The method is particularly attractive when the rational functions that determine the process have only few distinct poles zj∈C, because then few factorizations of matrices of the form A - zjI have to be computed. We discuss recursion relations for orthogonal bases of rational Krylov subspaces determined by rational functions with few distinct poles. These recursion formulas yield a new implementation of the rational Arnoldi process. Applications of the rational Arnoldi process to the approximation of matrix functions as well as to the computation of eigenvalues and pseudospectra of A are described. The new implementation is compared to several available implementations.
Eigenvalue; Matrix function; Pseudospectrum; Rational Arnoldi; Recursion relation; Algebra and number theory; Applied mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/183688
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