The Computation of Fixed Points and Applications (Lecture Notes in Economics and Mathematical Systems) - Couverture souple

Todd, M. J.

Couverture souple

ISBN 10 : 3540076859 ISBN 13 : 9783540076858

Editeur : Springer, 1976

Synopsis

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 1976
• Langue: anglais
• ISBN 10: 3540076859
• ISBN 13: 9783540076858
• Reliure: Broché
• Nombre de pages: 144
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne