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9780898714616 Academic Inspection Copy

Interative Solution of Nonlinear Equations in Several Variables

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"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 result 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 2 contains a 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.
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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