Summary#R##N#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.
['Miroslav S. Pranić', 'Lothar Reichel', 'Giuseppe Rodriguez', 'Zhengsheng Wang', 'Xuebo Yu']
A rational Arnoldi process with applications