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Numerical Stability and Sparsity in Piecewise-Linear Algorithms
Michael J. Todd
Pages 1-24 - Book chapterAbstract only
Two New Triangulations for Homotopy Fixed Point Algorithms with an Arbitrary Grid Refinement
Shlomo Shamir
Pages 25-56 - Book chapterAbstract only
Some Generic Properties of Paths Generated by Fixed Point Algorithms
D.G. Saari and Romesh Saigal
Pages 57-72 - Book chapterAbstract only
A Simple Reliable Numerical Algorithm for Following Homotopy Paths
Tien- Yien Li and James A. Yorke
Pages 73-91 - Book chapterAbstract only
Strongly Stable Stationary Solutions in Nonlinear Programs
Masakazu Kojima
Pages 93-138 - Book chapterAbstract only
Topological Perturbations in the Numerical Study of Nonlinear Eigenvalue and Bifurcation Problems
Hartmut Jürgens, Heinz-Otto Peitgen and Dietmar Saupe
Pages 139-181 - Book chapterAbstract only
General Equilibrium Analysis of Taxation Policy
John Whalley and John Piggott
Pages 183-195 - Book chapterAbstract only
Solving Urban General Equilibrium Models by Fixed Point Methods
James G. MacKinnon
Pages 197-212 - Book chapterAbstract only
Economic Equilibrium under Deformation of the Economy
Charles R. Engles
Pages 213-410 - Book chapterNo access
Index
Pages 411-413
About the book
Description
Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.
Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.
Details
ISBN
978-0-12-590240-3
Language
English
Published
1980
Copyright
Copyright © 1980 Elsevier Inc. All rights reserved.
Imprint
Academic Press