SIAM Homepage | Search Catalog | New Books | Author Index | Series Index | Title Index | View My Shopping Cart



The catalog and shopping cart are hosted for SIAM by EasyCart. Your transaction is secure. If you have any questions about your order, contact siambooks@siam.org.

Purchase Now!

Iterative Solution of Nonlinear Equations in Several VariablesIterative Solution of Nonlinear Equations in Several Variables

J. M. Ortega and W. C. Rheinboldt



Classics in Applied Mathematics 30

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.

Audience

Mathematicians and graduate students interested in systems of nonlinear equations and their computational solution will find this book a valuable introduction. Mechanical, chemical, and electrical engineers will also find this book useful. Readers should be familiar with advanced multivariate calculus and linear algebra.

Contents

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.

To request an examination copy or desk copy of this book, please use our online request form at www.siam.org/catalog/adopt.php.

2000 / xxvi + 572 pages / Softcover / ISBN-13: 978-0-898714-61-6 / ISBN-10: 0-89871-461-3 /
List Price $81.50 / SIAM Member Price $57.05 / Order Code CL30
Price
Quantity desired
   



Search our catalog for:

Shopping cart provided by: EasyCart.com
Select quantity and list or member price and then click the "Click to Order" button to add books to your shopping cart.
Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)