@article{46ca9fccd4ab480eadfa16c249bd905e,
title = "Decay in Functions of Multiband Matrices",
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.",
keywords = "Banded matrices, Exponential decay, Matrix functions, Multiband matrices, Multilevel matrices, Numerical range, Polynomial approximation, Toeplitz matrices",
author = "N. Mastronardi and M. Ng and Tyrtyshnikov, \{E. E.\}",
note = "Funding information: Istituto per le Applicazioni del Calcolo “M. Picone,” CNR, Sezione di Bari, 70126 Bari, Italy (
[email protected]). This author{\textquoteright}s work was supported by a Russian-Italian collaboration agreement between RAS and CNR. * Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (
[email protected]). This author{\textquoteright}s work was supported by RGC Research Grants Council grants and HKBU FRGs. § Institute of Numerical Mathematics, Russian Academy of Sciences, 11999, Moscow, Russia and Institute for Computational Mathematics, Hong Kong Baptist U niversity, Kowloon Tong, Hong Kong (
[email protected]). This author{\textquoteright}s work was supported by the Russian Foundation for Basic Research (RFBR 08-01-00115, RFBR/DFG 09-01-91332), Priority Research Grant of the Mathematical Sciences Department of the Russian Academy of Sciences, and Rus sian-Italian collaboration agreement between the Russian Academy of Sciences and CNR. Publisher copyright: Copyright {\textcopyright} 2010 Society for Industrial and Applied Mathematics",
year = "2010",
month = oct,
day = "7",
doi = "10.1137/090758374",
language = "English",
volume = "31",
pages = "2721--2737",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "5",
}