# Simplicial Algorithms on the Simplotope

• Timothy Mark Doup
Book

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 318)

1. Front Matter
Pages N2-VIII
2. ### Introduction and Definitions

1. Front Matter
Pages 1-1
2. Timothy Mark Doup
Pages 3-13
3. Timothy Mark Doup
Pages 15-44
4. Timothy Mark Doup
Pages 45-65
3. ### Algorithms on the Unit Simplex

1. Front Matter
Pages 67-67
2. Timothy Mark Doup
Pages 69-93
3. Timothy Mark Doup
Pages 95-110
4. Timothy Mark Doup
Pages 111-126
5. Timothy Mark Doup
Pages 127-133
4. ### Algorithms on the Simplotope

1. Front Matter
Pages 135-135
2. Timothy Mark Doup
Pages 137-158
3. Timothy Mark Doup
Pages 159-172
4. Timothy Mark Doup
Pages 173-195
5. Timothy Mark Doup
Pages 197-203
5. ### Continuous Deformation on the Simplotope

1. Front Matter
Pages 205-205
2. Timothy Mark Doup
Pages 207-254
6. Back Matter
Pages 255-264

### Introduction

1.1. Introduction Solving systems of nonlinear equations has since long been of great interest to researchers in the field of economics, mathematics, en­ gineering, 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.

### Keywords

#### Authors and affiliations

• Timothy Mark Doup
• 1
1. 1.Dept. of Mathematics and Systems EngineeringKoninklijke/Shell-Laboratorium, AmsterdamAmsterdamThe Netherlands

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-46651-9
• Copyright Information Springer-Verlag Berlin Heidelberg 1988
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-50233-3
• Online ISBN 978-3-642-46651-9
• Series Print ISSN 0075-8442
• Buy this book on publisher's site
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