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Full Description
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.
To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs or write their own based on the models included in the book.
Contents
Table of Pseudo Codes
Preface to the Classics Edition
Foreword
Chapter 1: Introduction
Chapter 2: The Basic Principles of Continuation Methods
Chapter 3: Newton's Method as Corrector
Chapter 4: Solving the Linear Systems
Chapter 5: Convergence of Euler-Newton-Like Methods
Chapter 6: Steplength Adaptations for the Predictor
Chapter 7: Predictor-Corrector Methods Using Updating
Chapter 8: Detection of Bifurcation Points Along a Curve
Chapter 9: Calculating Special Points of the Solution Curve
Chapter 10: Large Scale Problems
Chapter 11: Numerically Implementable Existence Proofs
Chapter 12: PL Continuation Methods
Chapter 13: PL Homotopy Algorithms
Chapter 14: General PL Algorithms on PL Manifolds
Chapter 15: Approximating Implicitly De¯ned Manifolds
Chapter 16: Update Methods and their Numerical Stability
Appendix 1: A Simple PC Continuation Method
Appendix 2: A PL Homotopy Method
Appendix 3: A Simple Euler Newton Update Method
Appendix 4: A Continuation Algorithm for Handling Bifurcation
Appendix 5: A PL Surface Generator
Appendix 6: SCOUT | Simplicial Continuation Utilities
Bibliography
Index and Notation.
