Estimation of u^T f(A)v for large-scale Unsymmetric Matrices
Abstract
Fast algorithms based on the unsymmetric look-ahead Lanczos and
the Arnoldi process are developed for the estimation of the
functional Phi(f)=u^T f(A)v for fixed u, v and
A, where A is a large-scale unsymmetric matrix. While
numerical results are presented which validate the comparable
accuracy of both approaches, the Arnoldi process, although in some
cases it may reach convergence more quickly, has greater memory
requirements, and may not be suitable for especially large
applications.
