Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices

Dušan M. Stipanović, Dragoslav D. Šiljak

Research output: Contribution to journalArticlepeer-review

Abstract

A natural generalization of the Jacobi and Gauss-Seidel iterations for interval systems is to allow the matrices to reside in convex polytopes. In order to apply the standard convergence criteria involving M-matrices to iterations for polytopic systems, we derive conditions for a convex polytope of matrices to be a polytope of M-matrices in terms of its vertices. We show how the conditions are used in the convergence analysis of iterations for block and nonlinear polytopic systems.

Original languageEnglish (US)
Pages (from-to)123-137
Number of pages15
JournalReliable Computing
Volume6
Issue number2
DOIs
StatePublished - 2000
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

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