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

摘要

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 polytipic systems.