Estimation of uTƒ(A)v for large-scale unsymmetric matrices.

Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional Φ(ƒ)=u^Tƒ(A) v for fixed u, v and A, where A∈ℜ^n×n is a large-scale unsymmetric matrix. Numerical results are presented which validate the comparable accuracy of both approaches. Although the Arnoldi process reaches convergence more quickly in some cases, it has greater memory requirements, and may not be suitable for especially large applications. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]