Parallel strategies for linear systems of equations

Abstract

This paper surveys new trends recently introduced in the most commonly occurring problems of linear algebra which will have a significant impact on all aspects of scientific computation and software development as it comes under pressure from the increasing advancement from parallel computing technology in its transition from sequential to parallel algorithmic techniques during the next decade.

Topics will include direct methods for dense matrices and alternating group explicit methods.

The computational analyses of the proposed strategies are presented which demonstrate that limited parallelism by using explicit block (2 × 2, 3 × 3) schemes can be effective in reducing data storage accesses in shared memory and communication in distributed parallel computer systems.

Keywords:

• Parallel algorithms
• WZ and PIE methods
• AGE method