Timothy M. Doup

Simplicial Algorithms on the Simplotope

• Broschiertes Buch

Produktbeschreibung

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.

---

Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Lecture Notes in Economics and Mathematical Systems 318
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-50233-3
• 1988.
• Seitenzahl: 276
• Erscheinungstermin: 14. September 1988
• Englisch
• Abmessung: 235mm x 155mm x 16mm
• Gewicht: 444g
• ISBN-13: 9783540502333
• ISBN-10: 3540502335
• Artikelnr.: 09201922

Inhaltsangabe

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.