Cover for Analysis and Computation of Fixed Points

Analysis and Computation of Fixed Points

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, May 7–8, 1979

Book1980

Edited by:

Stephen M. Robinson

Analysis and Computation of Fixed Points

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, May 7–8, 1979

Book1980

 

Cover for Analysis and Computation of Fixed Points

Edited by:

Stephen M. Robinson

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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 ... read full description

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  2. Book chapterAbstract only

    Numerical Stability and Sparsity in Piecewise-Linear Algorithms

    Michael J. Todd

    Pages 1-24

  3. Book chapterAbstract only

    Two New Triangulations for Homotopy Fixed Point Algorithms with an Arbitrary Grid Refinement

    Shlomo Shamir

    Pages 25-56

  4. Book chapterAbstract only

    Some Generic Properties of Paths Generated by Fixed Point Algorithms

    D.G. Saari and Romesh Saigal

    Pages 57-72

  5. Book chapterAbstract only

    A Simple Reliable Numerical Algorithm for Following Homotopy Paths

    Tien- Yien Li and James A. Yorke

    Pages 73-91

  6. Book chapterAbstract only

    Strongly Stable Stationary Solutions in Nonlinear Programs

    Masakazu Kojima

    Pages 93-138

  7. 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

  8. Book chapterAbstract only

    General Equilibrium Analysis of Taxation Policy

    John Whalley and John Piggott

    Pages 183-195

  9. Book chapterAbstract only

    Solving Urban General Equilibrium Models by Fixed Point Methods

    James G. MacKinnon

    Pages 197-212

  10. Book chapterAbstract only

    Economic Equilibrium under Deformation of the Economy

    Charles R. Engles

    Pages 213-410

  11. 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

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Editors

Stephen M. Robinson

Mathematics Research Center, University of Wisconsin—Madison, Madison, Wisconsin