On the order of convergence of preconditioned nonlinear conjugate gradient methods

M. Al-Baali, R. Fletcher

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)658-665
Number of pages8
JournalSIAM Journal on Scientific Computing
Volume17
Issue number3
Publication statusPublished - May 1996

Fingerprint

Conjugate gradient method
Order of Convergence
Conjugate Gradient Method
Hessian matrix
Line Search
Preconditioning
Newton Methods
Newton-Raphson method
Iteration

Keywords

  • Conjugate gradient methods
  • Newton's method
  • Preconditioning
  • Unconstrained optimization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the order of convergence of preconditioned nonlinear conjugate gradient methods. / Al-Baali, M.; Fletcher, R.

In: SIAM Journal on Scientific Computing, Vol. 17, No. 3, 05.1996, p. 658-665.

Research output: Contribution to journalArticle

@article{e22222f21fcf44809942cec0fd68421b,
title = "On the order of convergence of preconditioned nonlinear conjugate gradient methods",
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",
author = "M. Al-Baali and R. Fletcher",
year = "1996",
month = "5",
language = "English",
volume = "17",
pages = "658--665",
journal = "SIAM Journal of Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",

}

TY - JOUR

T1 - On the order of convergence of preconditioned nonlinear conjugate gradient methods

AU - Al-Baali, M.

AU - Fletcher, R.

PY - 1996/5

Y1 - 1996/5

N2 - 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.

AB - 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.

KW - Conjugate gradient methods

KW - Newton's method

KW - Preconditioning

KW - Unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=0038641529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038641529&partnerID=8YFLogxK

M3 - Article

VL - 17

SP - 658

EP - 665

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 3

ER -