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.
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.
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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2000 / xxvi + 572 pages / Softcover / ISBN-13: 978-0-898714-61-6 / ISBN-10: 0-89871-461-3 /
List Price $79.00 / SIAM Member Price $55.30 / Order Code CL30