### 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 |
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Pages (from-to) | 658-665 |

Number of pages | 8 |

Journal | SIAM Journal on Scientific Computing |

Volume | 17 |

Issue number | 3 |

Publication status | Published - May 1996 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Scientific Computing*,

*17*(3), 658-665.

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

Research output: Contribution to journal › Article

*SIAM Journal on Scientific Computing*, vol. 17, no. 3, pp. 658-665.

}

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 -