A direct method for solving linear systems

Abstract

In this work we propose a direct method for solving systems of linear equations which is based on a successive LU-decomposition of matrices of the form l + uv ^T . Simultaneously, the factors of an LU-decomposition of the coefficient matrix are obtained. A specific choice of the “rank-one decomposition” of the given matrix leads to a variant of the Gauss elimination process.

Keywords:

• LU-decomposition
• rank-decomposition

C.R. Categories:

• G.1.3
• F.2.1