ABS-Type Methods for Solving m Linear Equations in mk Steps for k = 1; 2; ... ;m [ABS-Type Methods for Solving m Linear Equations in mk Steps for k = 1; 2; ... ;m]

Abstract. The ABS methods, introduced by Abay, Broyden and Spedicato, are direct itera- tion methods for solving a linear system where the i-th iteration satises the rst i equations, therefore a system of m equations is solved in at most m steps. In this paper, we introduce a class of ABS-type methods for solving a full row rank linear equations, where the i-th itera- tion solves the rst 3i equations. We also extended this method for k steps. So, termination is achieved in at most h m+(k-1) k i steps. Morever in our new method in each iteration, we have the the general solution of each iteration.