Solving Large Sparse Linear Systems of Equations in a Vector Processing Environment.

摘要

The goal of the Phase I work was the development of V-PCGPAK, which will be a commercially available subroutine package of iterative techniques for solving very large, sparse, nonsymmetric systems of linear equations in a vector processing supercomputer environment. Since PCGPAK contains the iterative methods that are generally recognized as the best general-purpose sparse matrix iterative methods, objectives for Phase I were: (1) to implement vectorized production versions of the methods of PCGPAK, producing a preliminary version of V-PCGPAK; (2) to benchmark the package on realistic test problems; and (3) to compare the results with more fully vectorizable preconditioning methods. Results show that, without sacrificing the generality of the sparse matrix data structure of PCGPAK, researchers can achieve timings competitive with highly vectorizable implementations for special problems based on diagonal data structures.