Qualitative analysis of matrix splitting methods

I. Faragó, P. Tarvainen

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Qualitative properties of matrix splitting methods for linear systems with tridiagonal and block tridiagonal Stieltjes-Toeplitz matrices are studied. Two particular splittings, the so-called symmetric tridiagonal splittings and the bidiagonal splittings, are considered, and conditions for qualitative properties like nonnegativity and shape preservation are shown for them. Special attention is paid to their close relation to the well-known splitting techniques like regular and weak regular splitting methods. Extensions to block tridiagonal matrices are given, and their relation to algebraic representations of domain decomposition methods is discussed. The paper is concluded with illustrative numerical experiments.

Original languageEnglish
Pages (from-to)1055-1067
Number of pages13
JournalComputers and Mathematics with Applications
Volume42
Issue number8-9
DOIs
Publication statusPublished - Aug 24 2001

Fingerprint

Matrix Splitting
Splitting Method
Matrix Method
Qualitative Analysis
Tridiagonal matrix
Qualitative Properties
Domain decomposition methods
Shape Preservation
Block Tridiagonal Matrices
Linear systems
Nonnegativity
Toeplitz matrix
Domain Decomposition Method
Linear Systems
Numerical Experiment
Experiments

Keywords

  • Domain decomposition
  • Matrix splitting methods
  • Qualitative analysis
  • Regular and weak regular splittings
  • SOR method
  • Stieltjes-Toeplitz matrices

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Qualitative analysis of matrix splitting methods. / Faragó, I.; Tarvainen, P.

In: Computers and Mathematics with Applications, Vol. 42, No. 8-9, 24.08.2001, p. 1055-1067.

Research output: Contribution to journalArticle

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