A framework of conjugate direction methods for symmetric linear systems in optimization

Giovanni Fasano ()

No 31, Working Papers from Venice School of Management - Department of Management, Università Ca' Foscari Venezia

Abstract: In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method, in order to preserve the conjugacy. For specific values of the parameters in our framework we obtain schemes equivalent to both the CG and the scaled-CG. We also prove the finite convergence of the algorithms in CD, and we provide some error analysis. Finally, preconditioning is introduced for CD, and we show that standard error bounds for the preconditioned CG also hold for the preconditioned CD.

Keywords: Krylov-based Methods; Conjugate Direction Methods; Conjugacy Loss and Error Analysis; Preconditioning. (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2013-12
New Economics Papers: this item is included in nep-ore
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Related works:
Journal Article: A Framework of Conjugate Direction Methods for Symmetric Linear Systems in Optimization (2015)
Working Paper: A Framework of Conjugate Direction Methods for Symmetric Linear Systems in Optimization (2014)
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