Document Type
Book Review
Publication Date
2005
Keywords
Affine invariance, affine covariance
Abstract
In the context of solving nonlinear equations, the term "affine invariance" was introduced to describe the fact that when a function F: Rn → Rn is transformed to G = AF ,where A is an invertible matrix, then the equation F(x) = 0 has the same solutions as G(x) = 0, and the Newton iterates Xk+1 = Xk-F'(Xk)-1F(Xk) remain unchanged when F is replaced by G. The idea was that this property of Newton's method should be reflected in its convergence analysis and practical implementation, not only on aesthetic grounds but also because the resulting algorithms would likely be less sensitive to scaling, conditioning, and other numerical issues.
Publication Title
SIAM Review
Volume
47
Issue
2
First Page
401
Last Page
403
Required Publisher's Statement
Published by the Society for Industrial and Applied Mathematics
Courtesy of JSTOR
Stable URL: http://www.jstor.org/stable/20453655
Recommended Citation
Ypma, Tjalling, "Review of: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, by P. Deuflhard" (2005). Mathematics Faculty Publications. 94.
https://cedar.wwu.edu/math_facpubs/94
Subjects - Names (LCNAF)
Deuflhard, P. (Peter). Newton methods for nonlinear problems
Genre/Form
reviews (documents)
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
