Fixed Points

Algorithms and Applications

Stepan Karamardian

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780123980502
• eBook ISBN: 9781483261133
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann's iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

Table of contents

• Front Cover
• Fixed Points: Algorithms and Applications
• Copyright Page
• Table of Contents
• Contributors
• Preface
• Introduction
• Chapter 1. Finding Roots of Polynomials By Pivoting
• Chapter 2. A New Simplicial Approximation Algorithm With Restarts: Relations Between Convergence and Labelings
• Chapter 3. Complementary Pivot Theory and Markoviaïi Decision Chains
• Chapter 4. Application of a Fixed Point Search Algorithm to Nonlinear Boundary Value Problems Having Several Solutions
• Chapter 5. Generating Stationary Points for a Class of Mathematical Programming Problems by Fixed Point Algorithms
• Chapter 6. A Method of Continuation for Calculating a Brouwer Fixed Point
• Chapter 7. Continuation Methods for Simplicial Mappings
• Chapter 8. A Fixed Point Approach to Stability in Cooperative Games
• Chapter 9. Error Bounds for Approximate Fixed Points
• Chapter 10. Computation of Fixed Point in a Nonconvex Region
• Chapter 11. Investigations Into the Efficiency of the Fixed Point Algorithms
• Chapter 12. Almost-Complementary Paths in the Generalized Complementarity Problem
• Chapter 13. A Computational Comparison of Fixed Point Algorithms Which Use Complementary Pivoting
• Chapter 14. Computational Experience With Large-Scale Linear Complementarity Problems
• Chapter 15. Union Jack Triangulations
• Chapter 16. Fixed Point Iterations Using Infinite Matrices, III
• Chapter 17. Some Aspects of Mann's Iterative Method for Approximating Fixed Points
• Chapter 18. Solving Economic General Equilibrium Models by the Sandwich Method
• Chapter 19. Applying Fixed Point Algorithms to the Analysis of Tax Policies
• Chapter 20. "Fiscal Harmonization in the EEC; Some Preliminary Findings of Fixed Point Calculations"
• Chapter 21. Pricing for Congestion in Telephone Networks: A Numerical Example