A Parallel Processing Architecture for Solving Large-Scale Linear Systems

Solving linear systems with a large number of variables is at the core of many scienti c problems. Parallel processing techniques for solving such systems have received much attention in recent years. A pivotal theme in the literature pertains to the application of LU decomposing which factorizes an N N square matrix into two triangular matrices so that the resulting linear system can be more easily solved in O(N2 ) work. Inherently, the computational complexity of LU decomposition is O(N3 ). Moreover, it is a process that is challenging to parallelize. In this paper, we propose a highly-parallel methodology for solving large-scale dense linear systems by means of a novel application of Cramer's Rule. A numerically stable scheme is described, yielding an overall computational complexity of O(N) with N2 processing units.

• Type: Conference
• Year: 2008
• Where: PDPTA
• Authors: Arun Nagari, Itamar Elhanany, Ben Thompson, Fangxing Li, Thomas King
• Keywords: Computational Complexity, Distributed And Parallel Computing, Linear Systems, Parallel Processing Techniques, PDPTA 2008