Group lapped iterative technique for fast solution of large linear systems

Abstract

This work presents an iterative method for solving systems of linear equations. The technique is very much in the spirit of group iterative methods, allowing, however, lapped groups. For a wide class of matrices, the group lapped (GL) technique, herein introduced, improves the convergence rate by a large factor, demanding approximately the same number of operations per iteration as group iterative methods. For systems in which any subsystem is nonsingular and whose inverse matrix elements are null above (below) some upper (lower) diagonal, the exact solution is reached in just one step. Features of the GL method are illustrated with a numerical example.