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Numerical Continuation Methods
Eugene L. AllgowerKurt Georg
其他書名
An Introduction
出版Springer Berlin Heidelberg, 2011-10-05
主題Mathematics / Number SystemsBusiness & Economics / Economics / TheoryMathematics / Numerical Analysis
ISBN364261258X9783642612589
URLhttp://books.google.com.hk/books?id=nG-UoAEACAAJ&hl=&source=gbs_api
註釋Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.