A semi-iterative method for real spectrum singular linear systems with an arbitrary index

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:87

Article

Climent, JJ ; Neumann, M ; Sidi, A

关键词: singular systems;    iterative methods;    polynomial acceleration;   

DOI  :  10.1016/S0377-0427(97)00169-6

来源: Elsevier

【 摘 要 】

In this paper we develop a semi-iterative method for computing the Drazin-inverse solution of a singular linear system Ax=b, where the spectrum of A is real, but its index (i.e., the size of its largest Jordan block corresponding to the eigenvalue zero) is 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 determine eigenprojections onto generalized eigenspaces. Our treatment extends the work of Hanke and Hochbruck (1993) that considers the case in which the index of A is 1.

【 授权许可】

Free