Accelerating with rank-one updates

Abstract

AbstractConsider the iteration xk + 1 = xk + H(b> − Axk) for solving Ax = b (A is n x n nonsingular). We discuss rank-one updates to improve H as an approximation to A−1 during the iteration. The update kills and reduces singular values of I − AH and thus speeds up the convergence. The algorithm terminates after at most n sweeps, and if all n sweeps are needed, then A−1 has been computed