An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

Authors:
Roger B. Sidje;Kevin Burrage;B. Philippe
Affiliations:
Department of Mathematics, University of Queensland, Brisbane, QLD, Australia;Department of Mathematics, University of Queensland, Brisbane, QLD, Australia;INRIA/IRISA, Rennes Cedex, France
Venue:
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Year:
2003

Citing 6
Cited 0

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Topics in matrix analysis

Topics in matrix analysis
Analysis of some Krylov subspace approximations to the matrix exponential operator

SIAM Journal on Numerical Analysis
On Krylov Subspace Approximations to the Matrix Exponential Operator

SIAM Journal on Numerical Analysis
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions

SIAM Journal on Matrix Analysis and Applications
Rational Matrix Functions and Rank-1 Updates

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Lanczos algorithm is appreciated in many situations due to its speed and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.