A new multi-step ABS model to solve full row rank linear systems

ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress than corresponding Huang’s method. Also, these ABS-type models need less number of multiplications for a square system. In this paper, in order to economize and compress required space, we present a new three-step ABS procedure that is terminated in at most [((m+2))/3] steps. Computational complexity is considerable up to those corresponding Huang’s method and initial two-step ABS approaches. we present a new three-step ABS procedure that is terminated in at most [((m+2))/3] steps. Computational complexity is considerable up to those corresponding Huang’s method and initial two-step ABS approaches.