Newton Methods for Nonlinear Problems
Newton Methods for Nonlinear Problems
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DOI：
10.1007/978-3-642-23899-4
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
P. Deuflhard
中科院分区：
文献类型：
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作者：
P. Deuflhard
这本书讨论了科学和工程中具有挑战性的非线性问题的有效数值解，包括有限维(代数系统)和无限维(常微分方程式和偏微分方程式)。它的重点是用于正问题的局部和全局牛顿方法或用于反问题的高斯-牛顿方法。“仿射不变性”是指所提出的算法及其收敛分析在待解问题的仿射变换的四个子类中的一个子类下是不变的。与传统的教科书相比，区分仿射不变方法缩短了定理和证明，并允许构造完全自适应的算法。大量的数字插图、对比表格和练习使课文在计算数学课上很有用。同时，这本书为未来可能的研究开辟了许多方向。
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.