Simplicial Algorithms on the Simplotope: 318 (Lecture Notes in Economics and Mathematical Systems, 318) - Tapa blanda

Mark Doup, Timothy

 
9783540502333: Simplicial Algorithms on the Simplotope: 318 (Lecture Notes in Economics and Mathematical Systems, 318)
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ISBN 10: 3540502335 ISBN 13: 9783540502333
Editorial: Springer Berlin Heidelberg, 1988

Sinopsis

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.

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Reseña del editor

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.

Reseña del editor

This monograph deals with simplicial algorithms on the unit simplex and on the simplotope. Several new triangulations are introduced underlying the simplicial algorithms. The V-triangulation underlies a number of new simplicial algorithms and also underlies a continuous deformation algorithm on the simplotope. The monograph extensively discusses these algorithms and gives computational comparisons. The examples include exchange economies, quadratic programming, non-cooperative N-person games, and economies with a block diagonal supply-demand pattern. In the economic examples, the paths induced by the algorithms can be interpreted as price adjustment processes. These paths have the attractive feature that they always converge to an optimal solution.

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Editorial
Springer Berlin Heidelberg
Año de publicación
1988
Idioma
Inglés
ISBN 10 
3540502335
ISBN 13 
9783540502333
Encuadernación
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Número de páginas
276
Contacto del fabricante
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Otras ediciones populares con el mismo título

9780387502335: Simplicial Algorithms on the Simplotope (Lecture Notes in Economics & Mathematical Systems)

Edición Destacada

ISBN 10:  0387502335 ISBN 13:  9780387502335
Editorial: Springer Verlag, 1988
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