A New Bidirectional Cholesky Factorization Algorithm for Parallel Solution of Sparse Symmetric Positive Definite Systems

In this paper, we consider the problem of solving sparse linear systems occurring in finite difference applications (or N × N grid problems, N being the size of the linear system). We propose a new algorithm for the problem which is based on the Cholesky factorization, a symmetric variant of Gaussian elimination tailored to symmetric positive definite systems. The algorithm employs a new technique called bidirectional factorization to produce the complete solution vector by solving only one triangular system against two triangular systems in the existing Cholesky factorization after the factorization phase. The effectiveness of the new algorithm is demonstrated by comparing its performance with that of the existing Cholesky factorization for solving regular finite difference grid problems on hypercube multiprocessors.