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Some p-norm convergence results for Jacobi and Gauss-Seidel iterations
Palabras clave:
Jacobi method, Gauss-Seidel method, Systems of linear equations, Iterative solution, Convergence, Sassenfeld condition, 2000 Mathematics Subject Classification, Primary: 65F10 (en)Descargas
Abstract. Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It is well known that if (1) A satisfies the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D-1 A certifies certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the first result to irreducible matrices satisfying a weak Sassenfeld condition.
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