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.
Reliable Computing – Springer Journals
Published: Oct 7, 2004
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