A rational Arnoldi process with applications. Issue 6 (21st September 2016)

• Record Type: Journal Article
• Authors: Pranić, Miroslav S.; Reichel, Lothar; Rodriguez, Giuseppe; Wang, Zhengsheng; Yu, Xuebo
• Is Part Of: Numerical linear algebra with applications. Volume 23:Issue 6(2016:Nov.)
• Page Start: 1007
• Page End: 1022
• Publication Date: 2016-09-21
• Subjects: eigenvalue -- matrix function -- rational Arnoldi -- recursion relation -- pseudospectrum; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2065
• Languages: English
• ISSNs: 1070-5325

Abstract

Summary: The rational Arnoldi process is a popular method for the computation of a few eigenvalues of a large non‐Hermitian matrix A ∈ C n × 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 z j ∈ C, because then few factorizations of matrices of the form A − z j I 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.