ON THE EXISTENCE OF THE NEW QUADRANT INTERLOCKING FACTORIZATION FOR PARALLEL SOLUTION OF TRIDIAGONAL LINEAR-SYSTEMS

A direct parallel method, called new quadrant interlocking factorizati on (Q. I. F.) method for the solution of tridiagonal linear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity or the tridiagonal matrix is not the sufficient conditi on 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 th e nonsingularity. In this paper, we prove the existence of Q. I. F. wh en A is symmetric positive definite and also present the new version o f the proof of Kadalbajoo et al. [2].