Some p-norm convergence results forJacobi and Gauss-Seidel iterations

• Autores: Livinus U. Uko, Juan Carlos Orozco
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 38, Nº. 2, 2004, págs. 65-71
• Idioma: inglés
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• Resumen

  • 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-1A 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.