1. Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems.
- Author
-
Fasano, G.
- Subjects
- *
CONJUGATE gradient methods , *LANCZOS method , *APPROXIMATION theory , *NUMERICAL solutions to equations , *CONSTRAINED optimization , *MATHEMATICAL optimization , *LINEAR differential equations , *LINEAR systems , *ALGORITHMS - Abstract
This paper extends some theoretical properties of the conjugate gradient-type method FLR (Ref. 1) for iteratively solving indefinite linear systems of equations. The latter algorithm is a generalization of the conjugate gradient method by Hestenes and Stiefel (CG, Ref. 2).We develop a complete relationship between the FLR algorithm and the Lanczos process, in the case of indefinite and possibly singular matrices. Then, we develop simple theoretical results for the FLR algorithm in order to construct an approximation of the Moore-Penrose pseudoinverse of an indefinite matrix. Our approach supplies the theoretical framework for applications within unconstrained optimization. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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