Triangular Iterative Methods

Abstract

In this chapter we study implicit two-level iterative methods whose operators B correspond to triangular matrices. In Section 1 we look at the Gauss-Seidel method and formulate sufficient conditions for its convergence. In Section 2, the successive over-relaxation method is investigated. Here the choice of the iteration parameter is examined, and an estimate is obtained for the spectral radius of the transformation operator. In Section 3 a general matrix iterative scheme is investigated, selection of the iterative parameter is examined, and the method is shown to converge in H _A