Iterative Solution of Nonlinear Equations in Several Variables

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Overview

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.
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Editorial Reviews

Booknews
Originally published in 1970 by Academic Press. This unabridged reprint provides a survey of the theoretical results on systems of nonlinear equations in finite dimensions and the major iterative methods for their computational solution. While the field has developed since the book originally appeared, it remains a worthy background reference for the literature before 1970, particularly the section which contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780898714616
  • Publisher: SIAM
  • Publication date: 1/28/1987
  • Series: Classics in Applied Mathematics
  • Edition description: REPRINT
  • Pages: 572
  • Product dimensions: 5.98 (w) x 8.98 (h) x 1.18 (d)

Table of Contents

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