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

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. Content: Front Matter, Page iii Copyright, Page iv Contributors, Page vii Preface, Page ix, Stephen M. Robinson Numerical Stability and Sparsity in Piecewise-Linear Algorithms, Pages 1-24, Michael J. Todd Two New Triangulations for Homotopy Fixed Point Algorithms with an Arbitrary Grid Refinement, Pages 25-56, Shlomo Shamir Some Generic Properties of Paths Generated by Fixed Point Algorithms, Pages 57-72, D.G. Saari, Romesh Saigal A Simple Reliable Numerical Algorithm for Following Homotopy Paths, Pages 73-91, Tien- Yien Li, James A. Yorke Strongly Stable Stationary Solutions in Nonlinear Programs, Pages 93-138, Masakazu Kojima Topological Perturbations in the Numerical Study of Nonlinear Eigenvalue and Bifurcation Problems, Pages 139-181, Hartmut Jürgens, Heinz-Otto Peitgen, Dietmar Saupe General Equilibrium Analysis of Taxation Policy, Pages 183-195, John Whalley, John Piggott Solving Urban General Equilibrium Models by Fixed Point Methods, Pages 197-212, James G. MacKinnon Economic Equilibrium under Deformation of the Economy, Pages 213-410, Charles R. Engles Index, Pages 411-413 This volume contains the proceedings from the Symposium on Analysis and Computation of Fixed Points held at The University of Wisconsin--Madison on May 7-8, 1979. Held under the auspices of the Mathematics Research Center, sponsored by the National Science Foundation and the United States Army. There are eight papers addressing aspects of homotopy theory, algebraic topology, and the economic implications of computable general equilibrium models. The ninth paper is a doctoral dissertation, in hopes that its contents will reach interested researchers Edited By Stephen M. Robinson. Proceedings Of A Symposium Conducted By The Mathematics Research Center, The University Of Wisconsin--madison, May 7-8, 1979. Includes Bibliographical References And Index.