Some p-norm convergence results forJacobi and Gauss-Seidel iterations
Livinus U. Uko, Juan Carlos Orozco · Revista Colombiana de Matemáticas · 2004
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 satisfles the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D i1 A certifles certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the flrst result to irreducible matrices satisfying a weak Sassenfeld condition.