Jacobi and Gauss-Seidel iterations for polytopic systems: Convergence via convex \(M\)-matrices (Q1577435)
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scientific article; zbMATH DE number 1501472
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Jacobi and Gauss-Seidel iterations for polytopic systems: Convergence via convex \(M\)-matrices |
scientific article; zbMATH DE number 1501472 |
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Jacobi and Gauss-Seidel iterations for polytopic systems: Convergence via convex \(M\)-matrices (English)
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6 June 2001
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Linear interval equations are linear equations where the coefficient matrices range over a box. Common methods for solving such equations are Jacobi and Gauss-Seidel iterations. In the present paper, the coefficient matrices of the equations range over convex polytopes. It is shown that the Jacobi and Gauss-Seidel method converge if the matrices in the polytope are \(M\)-matrices. Conditions for a polytope matrix to contain ony \(M\)-matrices are derived. Further, generalizations of the investigations to block-matrices and nonlinear systems are discussed.
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convergence
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Jacobi method
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linear interval equations
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Gauss-Seidel method
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\(M\)-matrices
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polytope matrix
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block-matrices
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nonlinear systems
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