A Direct Method for Solving Linear Systems

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 I + uvr. 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. © 1987, Taylor & Francis Group, LLC. All rights reserved.