A projection method of the cimmino type for linear algebraic systems

Abstract

A projection method of the Cimmino type for the minimum norm solution of a system of linear algebraic equations Ax = b, where A is an m × n matrix, m ≤ n and rank(A) = m and where b ε R(A) the range of A is described. The algorithm converges provided certain practical estimations of the dominance of AA^T hold. It is shown that α = 1 is the optimal step-size choice for systems with AA^T k-diagonally dominant matrix with k ≥ 1. The algorithm in these cases converges fast also when A is not diagonally dominant. The algorithm, owing to its natural parallelism, is effectively implementable on vector computers such as CRAY-1 and CYBER 205 and on multiprocessors systems such as CRAY X-MP/48 and ALLIANT FX/80.