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-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.
Palabras claves. Jacobi method, Gauss-Seidel method, Systems of linear equations, Iterative
solution, Convergence, Sassenfeld condition
