Document Type
Journal Article
Department/Unit
Department of Mathematics
Title
Decay in functions of multiband matrices
Language
English
Abstract
The Benzi-Golub result on decay properties for matrix functions of a banded Hermitian matrix [BIT, 39 (1999), pp. 417-438] is extended to the case of multiband matrices. It is shown how the simple diagonal dominance technique applies to the general non-Hermitian case. We also present O(1) algorithms computing matrix functions of multiband and multi-Toeplitz (multilevel Toeplitz) matrices in time that depends on the bandwidth and prescribed approximation accuracy but does not depend on the size of matrices. © 2010 Society for Industrial and Applied Mathematics.
Keywords
Banded matrices, Exponential decay, Matrix functions, Multiband matrices, Multilevel matrices, Numerical range, Polynomial approximation, Toeplitz matrices
Publication Date
2010
Source Publication Title
SIAM Journal on Matrix Analysis and Applications
Volume
3
Issue
5
Start Page
2721
End Page
2737
Publisher
Society for Industrial and Applied Mathematics
DOI
10.1137/090758374
Link to Publisher's Edition
http://dx.doi.org/10.1137/090758374
ISSN (print)
08954798
ISSN (electronic)
10957162
Recommended Citation
Mastronardi, N., M. Ng, and E. E. Tyrtyshnikov. "Decay in functions of multiband matrices." SIAM Journal on Matrix Analysis and Applications 3.5 (2010): 2721-2737.