A cost effective graph-based partitioning algorithm for a system of linear equations Online publication date: Mon, 19-Mar-2018
by Hiroaki Yui; Satoshi Nishimura
International Journal of Computational Science and Engineering (IJCSE), Vol. 16, No. 2, 2018
Abstract: There are many techniques for reducing the number of operations in directly solving a system of sparse linear equations. One such method is nested dissection (ND). In numerical analysis, the ND algorithm heuristically divides and conquers a system of linear equations, based on graph partitioning. In this article, we present a new algorithm for the first level of such graph partitioning, which splits a graph into two roughly equalised subgraphs. The algorithm runs in almost linear time. We evaluate and discuss the solving costs by applying the proposed algorithm to various matrices.
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