Discrete mathematical models in the analysis of splitting iterative methods for linear systems

Splitting methods are used to solve most of the linear systems, Ax=bAx=b, when the conventional method of Gauss is not efficient. These methods use the factorization of the square matrix AA into two matrices MM and NN as A=M−NA=M−N where MM is nonsingular. Basic iterative methods such as Jacobi or Gauss–Seidel define the iterative scheme for matrices that have no zeros along its main diagonal.This paper is concerned with the development of an iterative method to approximate solutions when the coefficient matrix AA has some zero diagonal entries. The algorithm developed in this paper involves the analysis of a discrete-time descriptor system given by the equation Me(k+1)=Ne(k)Me(k+1)=Ne(k), e(k)e(k) being the error vector.