Use of Vector and Parallel Computers in the Solution of Large, Sparse Linear Equations

摘要

We discuss the direct solution of large, sparse linear equations on vector and parallel computers. To be specific, we examine algorithms based on Gaussian elimination for solving the equation Ax=b, when the coefficient matrix A is unsymmetric, large, and sparse. We will look at three classes of algorithms and comment on how effective they are at exploiting vector and parallel architectures. The classes into which we divide our algorithms are general methods, band and frontal techniques, and multifrontal approaches. 32 refs., 2 figs., 5 tabs. (ERA citation 12:022056)