Topological decomposition algorithm for optimized solution of a system of linear equations

Abstract

A number of techniques for the direct solution of large systems of linear equations have been developed. Some of them are widely known and used for non-sparse systems of linear equations: LU decomposition and Cholesky decomposition. On the other hand, for sparse matrices, there are different types of algorithms, which decompose a system of linear equations into a number of subsets of the system. However, in the past there is no discussion for algorithms to decompose a large system of linear equations. In this article, we propose an efficient decomposition algorithm to optimize total operation costs using graph theory.