Two-sided bounds on the inverses of diagonally dominant tridiagonal matrices

Authors
Nabben, R
Citation
R. Nabben, Two-sided bounds on the inverses of diagonally dominant tridiagonal matrices, LIN ALG APP, 287(1-3), 1999, pp. 289-305
Citations number
20
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
00243795 → ACNP
Volume
287
Issue
1-3
Year of publication
1999
Pages
289 - 305
Database
ISI
SICI code
0024-3795(19990115)287:1-3<289:TBOTIO>2.0.ZU;2-R
Abstract
We establish upper and lower bounds for the entries of the inverses of diag onally dominant tridiagonal matrices. These bounds improve the bounds recen tly given by Shivakumar and Ji. Moreover, we show how to improve our bounds iteratively. For an nxn M-matrix this iterative refinement yields the exac t inverse after n - 1 steps. (C) 1999 Elsevier Science Inc. All rights rese rved.