The Computation of Fixed Points and Applications
Seiten
1976
|
1976
Springer Berlin (Verlag)
978-3-540-07685-8 (ISBN)
Springer Berlin (Verlag)
978-3-540-07685-8 (ISBN)
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.
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.
Erscheint lt. Verlag | 1.5.1976 |
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Reihe/Serie | Lecture Notes in Economics and Mathematical Systems |
Zusatzinfo | VII, 132 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 140 x 216 mm |
Gewicht | 260 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
Wirtschaft ► Betriebswirtschaft / Management | |
Schlagworte | Computation • Economic Growth • Economics • Game Theory • Invariant |
ISBN-10 | 3-540-07685-9 / 3540076859 |
ISBN-13 | 978-3-540-07685-8 / 9783540076858 |
Zustand | Neuware |
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