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

• Published in: Numerical linear algebra with applications Vol. 11; no. 1; pp. 75 - 89
• Main Authors: Guo, Hongbin, Renaut, Rosemary A.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.02.2004
• Subjects: Arnoldi; large-scale unsymmetric matrix; look-ahead Lanczos; matrix function
• ISSN: 1070-5325; 1099-1506; 1099-1506
• DOI: 10.1002/nla.334

Fast algorithms, based on the unsymmetric look‐ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional Φ(ƒ)=uTƒ(A) v for fixed u, v and A, where A∈ℜ︁n×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.