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

Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

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

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009961021112
Publisher site
See Article on Publisher Site

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

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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