Reliable Computing

, Volume 6, Issue 2, pp 123–137 | Cite as

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

  • Dušan M. Stipanović
  • Dragoslav D. Šiljak


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 the conditions are used in the convergence analysis of iterations for block and nonlinear polytopic systems.


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Dušan M. Stipanović
    • 1
  • Dragoslav D. Šiljak
    • 2
  1. 1.Department of Electrical EngineeringSanta Clara UniversitySanta ClaraUSA
  2. 2.B & M Swig Professor, School of EngineeringSanta Clara UniversitySanta ClaraUSA

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