Technical Report CS0868

TR#:CS0868
Class:CS
Title: A SEMI--ITERATIVE METHOD FOR SINGULAR LINEAR SYSTEMS WITH ARBITRARY INDEX.
Authors: J-J. Climent, M. Neumann and A. Sidi
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Abstract: In this paper we develop a semi--iterative method for computing the Drazin-inverse solution of a singular linear system $Ax=b$, where the index of the matrix $A$ may be arbitrary. The method employs a set of polynomials that satisfy certain normalization conditions and minimize some well defined least squares norm. We develop an efficient recursive algorithm for implementing this method that has a fixed length independent of the index of $A$. Following that, we give a complete theory of convergence, in which we provide rates of convergence as well. We conclude with a numerical application to determining an eigenprojection. Our treatment extends the work of Hanke and Hochbruck (1993) that considers the case in which the index of $A$ is unity.
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