The Computation of Fixed Points and Applications (Paperback, 1976 ed.)

Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore via triangu- tions. For this reason, Scarf is cited less in this manuscript than his contri- tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixed-point methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixed-point algorithms to find many solutions to boundary-value problems.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Economics and Mathematical Systems, 124
Release date:	May 1976
First published:	1976
Authors:	M. J. Todd
Dimensions:	216 x 140 x 8mm (L x W x T)
Format:	Paperback
Pages:	132
Edition:	1976 ed.
ISBN-13:	978-3-540-07685-8
Categories:	Books > Business & Economics > Business & management > General Books > Science & Mathematics > Mathematics > Topology > General
LSN:	3-540-07685-9
Barcode:	9783540076858

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