On the order of convergence of preconditioned nonlinear conjugate gradient methods

被引：10

作者：

AlBaali, M ^{[1
]}

Fletcher, R ^{[1
]}

机构：

[1] UNIV DUNDEE, DEPT MATH & COMP SCI, DUNDEE DD1 4HN, SCOTLAND

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1996年 / 17卷 / 03期

关键词：

unconstrained optimization; Newton's method; conjugate gradient methods; preconditioning;

D O I：

10.1137/S1064827591194303

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：658 / 665

页数：8

共 6 条

[1]

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[2]

Fletcher R., 2013, Practical Methods of Optimization, DOI [10.1002/9781118723203, DOI 10.1002/9781118723203]

[3]

Ortega J.M, 1970, CLASSICS APPL MATH

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[5]

RUBE A, 1979, BIT, V19, P356

[6] ORDERS OF CONVERGENCE FOR ITERATIVE PROCEDURES [J].

VOIGT, RG .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1971, 8 (02) :222-&

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