A PARALLEL PRECONDITIONED CONJUGATE-GRADIENT PACKAGE FOR SOLVING SPARSE LINEAR-SYSTEMS ON A CRAY Y-MP

In this paper we discuss current activities at Cray Research to develop general-purpose, production-quality software for the efficient solution of sparse linear systems. In particular, we discuss our development of a package of iterative methods that includes conjugate gradient and related methods (GMRES, ORTHOMIN and others) along with several preconditioners (incomplete Cholesky and LU factorization and polynomial). Vector and parallel performance issues are discussed as well as package design. Also, benchmarks on a wide variety of real-life problems are presented to assess the robustness and performance of methods implemented in our software. For symmetric positive-definite problems, we also compare the performance of the preconditioned conjugate gradient code with our parallel implementation of the multifrontal method for sparse Cholesky factorization.