On the Implicit Deflation of Nearly Singular Systems of Linear Equations

Abstract

In solving the linear system $Ax = b$ when A is nearly singular, it is often appropriate to work in a coordinate system in which the singularity can be easily removed. When A is large and sparse, an explicit transformation of the system cannot be made, since it will destroy the sparsity of the system. In this paper, an algorithm similar to the method of iterative refinement for linear systems is given and its numerical properties described.