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A new investigation of the extended Krylov subspace method for matrix function evaluations
Author(s) -
Knizhnerman L.,
Simoncini V.
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.652
Subject(s) - krylov subspace , mathematics , subspace topology , rate of convergence , generalized minimal residual method , matrix (chemical analysis) , convergence (economics) , function (biology) , matrix function , algorithm , mathematical optimization , iterative method , symmetric matrix , computer science , mathematical analysis , eigenvalues and eigenvectors , computer network , channel (broadcasting) , materials science , physics , quantum mechanics , evolutionary biology , economics , composite material , biology , economic growth
For large square matrices A and functions f , the numerical approximation of the action of f ( A ) to a vector v has received considerable attention in the last two decades. In this paper we investigate the extended Krylov subspace method , a technique that was recently proposed to approximate f ( A ) v for A symmetric. We provide a new theoretical analysis of the method, which improves the original result for A symmetric, and gives a new estimate for A nonsymmetric. Numerical experiments confirm that the new error estimates correctly capture the linear asymptotic convergence rate of the approximation. By using recent algorithmic improvements, we also show that the method is computationally competitive with respect to other enhancement techniques. Copyright © 2009 John Wiley & Sons, Ltd.