The Computation of Fixed Points and Applications - Bookswagon
The Computation of Fixed Points and Applications

The Computation of Fixed Points and Applications


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About the Book

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.


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Product Details
  • ISBN-13: 9783540076858
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 1976 ed.
  • Language: English
  • Returnable: Y
  • Spine Width: 8 mm
  • Width: 140 mm
  • ISBN-10: 3540076859
  • Publisher Date: 01 May 1976
  • Binding: Paperback
  • Height: 216 mm
  • No of Pages: 132
  • Series Title: Lecture Notes in Economic and Mathematical Systems
  • Weight: 222 gr


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