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＜電子ブック＞
The Computation of Fixed Points and Applications / by M. J. Todd
(Lecture Notes in Economics and Mathematical Systems. ISSN:21969957 ; 124)

版	1st ed. 1976.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1976
大きさ	VII, 132 p : online resource
著者標目	*Todd, M. J author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Business LCSH:Management science FREE:Topology FREE:Business and Management
一般注記	I Brouwer’s Theorem -- II Some Applications of Brouwer’s Theorem -- III Triangulations -- IV Algorithms to Find Completely-Labelled Simplices -- V Extensions of Brouwer’s Theorem -- VI Applications of Kakutani’s Theorem and its Extensions -- VII Eaves’ First Algorithm -- VIII Merrill’s Algorithm -- IX Homotopy Algorithms -- X Triangulations with Continuous Refinement of Grid Size -- XI Measures of Efficiency for Triangulations -- References 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 HTTP:URL=https://doi.org/10.1007/978-3-642-50327-6

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