非線形問題のためのニュートン法 Newton Methods for Nonlinear Problems : Affine Invariance and Adaptive Algorithms (Springer Series in Computational Mathematics) 〈Vol. 35〉

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非線形問題のためのニュートン法<br>Newton Methods for Nonlinear Problems : Affine Invariance and Adaptive Algorithms (Springer Series in Computational Mathematics) 〈Vol. 35〉

非線形問題のためのニュートン法
Newton Methods for Nonlinear Problems : Affine Invariance and Adaptive Algorithms (Springer Series in Computational Mathematics) 〈Vol. 35〉

Deuflhard, Peter

Springer（2011/12発売）

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製本 Paperback:紙装版/ペーパーバック版／ページ数 424 p.／サイズ 49 illus.
商品コード 9783642238987

基本説明

New in softcover. Hardcover was published in 2004.

Full Description

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.