Simplicial Algorithms on the Simplotope

by Timothy M. Doup

Overview

1.1. Introduction Solving systems of nonlinear equations has since long been of great interest to researchers in the field of economics, mathematics, engineering, and many other professions. Many problems such as finding an equilibrium, a zero point, or a fixed point, can be formulated as the problem of finding a solution to a system of nonlinear equations. There are many methods to solve the nonlinear system such as Newton's method, the homotopy method, and the simplicial method. In this monograph we mainly consider the simplicial method. Traditionally, the zero point and fixed point problem have been solved by iterative methods such as Newton's method and modifications thereof. Among the difficulties which may cause an iterative method to perform inefficiently or even fail are: the lack of good starting points, slow convergence, and the lack of smoothness of the underlying function. These difficulties have been partly overcome by the introduction of homo­ topy methods.

Product Details

ISBN-13:	9783540502333
Publisher:	Springer Berlin Heidelberg
Publication date:	10/17/1988
Series:	Lecture Notes in Economics and Mathematical Systems , #318
Edition description:	Softcover reprint of the original 1st ed. 1988
Pages:	262
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

I Introduction and Definitions.- 1. Introduction.- 2. Definitions and Existence Theorems.- 3. Triangulations of Sn and S.- II Algorithms on the Unit Simple.- 4. An introduction to Simplicial Algorithms on the Unit Simplex.- 5. The (2n+1-2)-Ray Algorithm.- 6. The 2-Ray Algorithm.- 7. Comparisons and Computational Results.- III Algorithms on the Simplotope.- 8. An Introduction to Simplicial Algorithms on the Simplotope.- 9. The Product-Ray Algorithm.- 10. The Exponent-Ray Algorithm.- 11. Comparisons and Computational Results.- IV Continuous Deformation on the Simplotope.- 12. The Continuous Deformation Algorithm on the Simplotope.- References.