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

Stephen M. Robinson

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483266022
• Topic: Mathematics
• Subtopic: Topology
• Index: 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.

Table of contents

• Front Cover
• Analysis and Computation of Fixed Points
• Copyright Page
• Table of Contents
• Contributors
• Preface
• Chapter 1. Numerical Stability and Sparsity in Piecewise-Linear Algorithms
• Chapter 2. Two New Triangulations for Homotopy Fixed Point Algorithms with an Arbitrary Grid Refinement
• Chapter 3. Some Generic Properties of Paths Generated by Fixed Point Algorithms
• Chapter 4. A Simple Reliable Numerical Algorithm for Following Homotopy Paths
• Chapter 5. Strongly Stable Stationary Solutions in Nonlinear Programs
• Chapter 6. Topological Perturbations in the Numerical Study of Nonlinear Eigenvalue and Bifurcation Problems
• Chapter 7. General Equilibrium Analysis of Taxation Policy
• Chapter 8. Solving Urban General Equilibrium Models by Fixed Point Methods
• Chapter 9. Economic Equilibrium under Deformation of the Economy
• Index