A NEW PROOF OF SUPERLINEAR CONVERGENCE FOR BROYDEN'S METHOD IN HILBERT SPACE

被引：14

作者：

Kelley, C. T. ^{[1
]}

Sachs, E. W. ^{[2
]}

机构：

[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Univ Trier, FB Math 4, D-5500 Trier, Germany

来源：

SIAM JOURNAL ON OPTIMIZATION | 1991年 / 1卷 / 01期

基金：

美国国家科学基金会;

关键词：

Broyden's method; superlinear convergence; collective compactness;

D O I：

10.1137/0801011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Broyden's method is an extension of the secant method for an equation in one real variable to an arbitrary Hilbert space setting. It is a result of Griewank that the Broyden iterates converge locally superlinearly to a root if, in addition to the assumptions needed in finite dimension, the initial approximation for the Frechet derivative differs from the Frechet derivative at the root only by a compact operator. In this paper a new and much simpler proof of this theorem is given based on the concept of collective compactness.

引用

页码：146 / 150

页数：5

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