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

Hongbin Guo; Rosemary Renaut

doi:10.1002/nla.334

Estimation of u^T f(A )v for large-scale unsymmetric matrices

Hongbin Guo, Rosemary Renaut

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional φ(f) = u^Tf(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.

Original language	English (US)
Pages (from-to)	75-89
Number of pages	15
Journal	Numerical Linear Algebra with Applications
Volume	11
Issue number	1
DOIs	https://doi.org/10.1002/nla.334
State	Published - Feb 1 2004

Keywords

Arnoldi
Large-scale unsymmetric matrix
Look-ahead Lanczos
Matrix function

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

Access to Document

10.1002/nla.334

Cite this

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abstract = "Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional φ(f) = uTf(A)v for fixed u,v and A, where A ∈ Rn×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.",

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AB - Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional φ(f) = uTf(A)v for fixed u,v and A, where A ∈ Rn×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.

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