A rational Arnoldi process with applications. Issue 6 (21st September 2016) - Pranić, Miroslav S.; Reichel, Lothar; Rodriguez, Giuseppe; Wang, Zhengsheng; Yu, Xuebo
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.