Vectorized General Sparsity Algorithms with Backing Store.

摘要

The direct solution of large, sparse unsymmetric sets of simultaneous equations is commonly involved in the numerical solution of algebraic, differential, and partial differential equations. This report describes two new clases of computational algorithms for the solution of such equations. Each algorithm detects matrix structure suitable for vector processing and, potentially, for faster processing on cache machines. One procedure favors structure usually associated with small sparse matrices; one is directed toward sets of equations requiring a large backing store. Comparisons of timing (on a chache machine) and of memory requirements are made between these new procedures and existing general sparsity techniques for a variety of science-engineering examples. Issues related to implementation are given for software implementations of the two algorithms. (Author)