Contemporary Algorithms for Solving Problems in Economics and Other Disciplines


Ioannis K. Argyros
Cameron University, Department of Mathematical Sciences, Lawton, OK, USA

Samundra Regmi
Cameron University, Department of Mathematical Sciences, Lawton, Oklahoma, USA

Series: Mathematics Research Developments
BISAC: MAT027000

Numerous problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use algorithms which seems to be the only alternative.

Due to the explosion of technology, scientific and parallel computing, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. There is exactly where we come in with our book containing such algorithms with application especially in problems from Economics but also from other areas such as Mathematical: Biology, Chemistry, Physics, Scientific, Parallel Computing, and also Engineering.

The book can be used by senior undergraduate students, graduate students, researchers and practitioners in the aforementioned area in the class room or as a reference material. Readers should know the fundamentals of numerical functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to the readers. (Imprint: Nova)



Table of Contents


Chapter 1. Definition, Existence and Uniqueness of Equilibrium in Oligopoly Markets

Chapter 2. Numerical Methodology for Solving Oligopoly Problems

Chapter 3. Global Convergence of Iterative Methods with Inverses

Chapter 4. Ball Convergence of Third and Fourth Order Methods for Multiple Zeros

Chapter 5. Local Convergence of Two Methods for Multiple Roots Eight Order

Chapter 6. Choosing the Initial Points for Newton’s Method

Chapter 7. Extending the Applicability of an Ulm-Like Method under Weak Conditions

Chapter 8. Projection Methods for Solving Equations with a Non-differentiable Term

Chapter 9. Efficient Seventh Order of Convergence Solver

Chapter 10. An Extended Result of Rall-Type for Newton’s Method

Chapter 11. Extension of Newton’s Method for Cone Valued Operators

Chapter 12. Inexact Newton’s Method under Robinson’s Condition

Chapter 13. Newton’s Method for Generalized Equations with Monotone Operators

Chapter 14. Convergence of Newton’s method and uniqueness of the solution for Banach Space Valued Equations

Chapter 15. Convergence of Newton’s method and uniqueness of the solution for Banach Space Valued Equations II

Chapter 16. Extended Gauss-Newton Method: Convergence and Uniqueness Results

Chapter 17. Newton’s Method for Variational Problems: Wang’s g-condition and Smale’s a-theory

Chapter 18. Extending the Applicability of Newton’s Method

Chapter 19. On the Convergence of a Derivative Free Method using Recurrent Functions

Chapter 20. Inexact Newton-like Method under Weak Lipschitz Conditions

Chapter 21. Ball Convergence Theorem for Inexact Newton Methods in Banach Space

Chapter 22. Extending the Semi-Local Convergence of a Stirling-Type Method

Chapter 23. Newton’s Method for Systems of Equations with Constant Rank Derivatives

Chapter 24. Extended Super-Halley Method

Chapter 25. Chebyshev-Type Method of Order Three

Chapter 26. Extended Semi-Local Convergence of the Chebyshev-Halley Method

Chapter 27. Gauss-Newton-Type Schemes for Undetermined Least Squares Problems

Glossary of Symbols

Additional information