Parallel solution of large symmetric tridiagonal linear systems

摘要

We present a matrix factorization called WZ factorization for the solution of symmetric tridiagonal linear systems. When combined with partitioning scheme, it renders a divide and conquer algorithm. Existence theorems are presented and backward error analysis is given. A variant of WZ factorization called WDZ factorization is also presented. Both WZ and WDZ algorithms for parallel solution of large tridiagonal symmetric positive definite linear systems are implemented on parallel machine with MPI as inter node communication.