Front cover image for Introduction to numerical continuation methods

Introduction to numerical continuation methods

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. The book 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. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful
eBook, English, 2003
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), Philadelphia, Pa., 2003
1 online resource (xxv, 388 pages) : illustrations.
9780898719154, 0898719151
The basic principles of continuation methods
Newton's method as corrector
Solving the linear systems
Convergence of Euler-Newton-like methods
Steplength adaptations for the predictor
Predictor-corrector methods using updating
Detection of bifurcation points along a curve
Calculating special points of the solution curve
Large scale problems
Numerically implementable existence proofs
PL continuation methods
PL homotopy algorithms
General PL algorithms on PL manifolds
Approximating implicitly defined manifolds
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
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