On the order of convergence of preconditioned nonlinear conjugate gradient methods

M. Al-Baali; R. Fletcher

doi:10.1137/S1064827591194303

On the order of convergence of preconditioned nonlinear conjugate gradient methods

M. Al-Baali^*, R. Fletcher

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

An analysis is given of preconditioned nonlinear conjugate gradient methods in which the preconditioning matrix is the exact Hessian matrix at each iteration (or a nearby matrix). It is shown that the order of convergence of certain preconditioned methods is less than that of Newton's method when exact line searches are used, and an example is given.

Original language	English
Pages (from-to)	658-665
Number of pages	8
Journal	SIAM Journal on Scientific Computing
Volume	17
Issue number	3
DOIs	https://doi.org/10.1137/S1064827591194303
Publication status	Published - May 1996

Keywords

Conjugate gradient methods
Newton's method
Preconditioning
Unconstrained optimization

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1137/S1064827591194303

Cite this

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abstract = "An analysis is given of preconditioned nonlinear conjugate gradient methods in which the preconditioning matrix is the exact Hessian matrix at each iteration (or a nearby matrix). It is shown that the order of convergence of certain preconditioned methods is less than that of Newton's method when exact line searches are used, and an example is given.",

keywords = "Conjugate gradient methods, Newton's method, Preconditioning, Unconstrained optimization",

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KW - Newton's method

KW - Preconditioning

KW - Unconstrained optimization

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On the order of convergence of preconditioned nonlinear conjugate gradient methods

Abstract

Keywords

ASJC Scopus subject areas

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