## Browse content

### Table of contents

#### Actions for selected chapters

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- Book chapterAbstract only
#### 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