On the existence of the new quadrant interlocking factorization for parallel solution of tridiagonal linear systems

Abstract

A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I. F. method when A is diagonally dominant in addition to the nonsingularity. In this paper, we prove the existence of Q. I. F. when A is symmetric positive definite and also present the new version of the proof of Kadalbajoo et al. [2].