A faster algorithm for solving linear algebraic equations on the star graph

Abstract

The problem of solving a linear system of equations is widely encountered in many fields of science and engineering. In this paper, we present a parallel algorithm to solve the above problem on a star graph. The proposed solution (i) is based on a variant of the Gaussian elimination algorithm (GE) called the successive Gaussian elimination algorithm (SGE) (IEE Proc. Comput. Digit. Tech. 143 (4) (1996)) and (ii) supports partial pivoting to provide numerical stability. We present efficient matrix distribution techniques on the star graph. Our proposed parallel algorithm employs these techniques to reduce communication overhead during matrix operations on the star graph. We estimate the performance of our parallel algorithm and demonstrate its effectiveness by comparing it with a recent algorithm for the same problem on star graphs (IEEE Trans. Parallel Distrib. Systems 8 (8) (1997) 803).