Iterative Solution of Nonlinear Equations in Several Variables pdf epub mobi txt 电子书下载 2025

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出版者:Society for Industrial and Applied Mathematics

作者:J. M. Ortega

出品人:

页数:598

译者:

出版时间:1987-1-1

价格:GBP 84.50

装帧:Paperback

isbn号码:9780898714616

丛书系列:Classics in Applied Mathematics

图书标签:

nonlinear
iin
equatons
Iterative
variabl
solution
several
of
非线性方程
迭代方法
多变量
数值分析
优化算法
数学模型
科学计算
工程数学
数值解
迭代求解

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具体描述

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time.

Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.

作者简介

James M. Ortega Florida Institute of Technology, Melbourne, Fl

Werner C. Rheinboldt Univ. of Pittsburgh, Pittsburgh, PA

目录信息

Preface to the Classics Edition
Preface
Acknowledgments
Glossary of Symbols
Introduction
Part I: Background Material.
Chapter 1: Sample Problems
Chapter 2: Linear Algebra
Chapter 3: Analysis
Part II: Nonconstructive Existence Theorems.
Chapter 4: Gradient Mappings and Minimization
Chapter 5: Contractions and the Continuation Property
Chapter 6: The Degree of a Mapping
Part III: Iterative Methods.
Chapter 7: General Iterative Methods
Chapter 8: Minimization Methods
Part IV: Local Convergence.
Chapter 9: Rates of Convergence-General
Chapter 10: One-Step Stationary Methods
Chapter 11: Multistep Methods and Additional One-Step Methods
Part V: Semilocal and Global Convergence.
Chapter 12: Contractions and Nonlinear Majorants
Chapter 13: Convergence under Partial Ordering
Chapter 14: Convergence of Minimization Methods
An Annotated List of Basic Reference Books
Bibliography
Author Index
Subject Index.
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