Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems

Giovanni Fasano ()

Journal of Optimization Theory and Applications, 2007, vol. 132, issue 2, No 3, 267-285

Abstract: 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.

Keywords: Unconstrained optimization; Krylov subspace methods; planar conjugate gradient; Moore-Penrose pseudoinverse (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-006-9119-3

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