Contemporary Algorithms for Solving Problems in Economics and Other Disciplines
Published on 10. July 2020
325 pages
978-1-5361-8129-6 (ISBN)
Description
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.
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07/2020
Nova Science Publishers Inc
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Content
- Intro
- CONTEMPORARY ALGORITHMSFOR SOLVING PROBLEMS INECONOMICS AND OTHERDISCIPLINES
- CONTEMPORARY ALGORITHMSFOR SOLVING PROBLEMS INECONOMICS AND OTHERDISCIPLINES
- Contents
- Preface
- Chapter 1Definition, Existence andUniqueness of Equilibriumin OligopolyMarkets
- 1. Introduction
- 2. The Multi-Product Oligopoly Game
- 3. Relation of the Equilibrium Problems to Fixed PointProblems
- 4. Relation of Equilibrium Problems toNonlinear Complexity Problems in theMulti-Product Oligopoly Game
- References
- Chapter 2NumericalMethodology forSolving Oligopoly Problems
- 1. Introduction
- 2. Multi-Product Oligopoly Game
- 3. Reduction to Optimization Problems
- 4. Direct Solution of Governing Equations
- 5. Solution of Nonlinear Complementarity Problems
- 6. The Classical Oligopoly Game
- Constructive Proof of Theorem 2.1 from Chapter 1.
- References
- Chapter 3Global Convergence of IterativeMethods with Inverses
- 1. Introduction
- 2. Preliminaries
- 3. Global Convergence
- 4. Uniqueness of the Solution
- References
- Chapter 4Ball Convergence of Third andFourth Order Methods forMultiple Zeros
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 5Local Convergence of TwoMethods For Multiple RootsEight Order
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 6Choosing the Initial Points forNewton's Method
- 1. Introduction
- 2. Semi-Local Convergence
- References
- Chapter 7Extending the Applicability ofan Ulm-Like Method underWeak Conditions
- 1. Introduction
- 2. Semi-Local Convergence
- References
- Chapter 8Projection Methods for SolvingEquations with aNon-Differentiable Term
- 1. Introduction
- 2. Convergence Results
- 3. Applications
- References
- Chapter 9Efficient Seventh Order ofConvergence Solver
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 10An Extended Result ofRall-Type for Newton's Method
- 1. Introduction
- 2. New Convergence Analysis
- References
- Chapter 11Extension of Newton's Methodfor Cone Valued Operators
- 1. Introduction
- 2. Convergence of the Algorithm
- References
- Chapter 12Inexact Newton's Method underRobinson's Condition
- 1. Introduction
- 2. Semi-Local Analysis
- References
- Chapter 13Newton's Method forGeneralized Equations withMonotoneOperators
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 14Convergence of Newton'sMethod and Uniqueness of theSolution for Banach SpaceValued Equations
- 1. Introduction
- 2. Convergence
- 3. Uniqueness of the Solution
- References
- Chapter 15Convergence of Newton'sMethod and Uniqueness of theSolution for Banach SpaceValued Equations II
- 1. Introduction
- References
- Chapter 16Extended Gauss-NewtonMethod: Convergence andUniqueness Results
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 17Newton's Method forVariational Problems: Wang'sg-Condition and Smale'sa-Theory
- 1. Introduction
- 2. Local Convergence
- 3. Convergence Connected to a-Theory
- 4. Convergence and Analytic Mapping
- References
- Chapter 18Extending the Applicability ofNewtons Method
- 1. Introduction
- 2. Analysis
- 3. Numerical Examples
- References
- Chapter 19On the Convergence of aDerivative Free Method UsingRecurrent Functions
- 1. Introduction
- 2. Semilocal Convergence Analysis for (STM)
- 3. Numerical Example
- References
- Chapter 20Inexact Newton-Like MethodunderWeak LipschitzConditions
- 1. Introduction
- 2. Background
- 3. Local Convergence
- 4. Special Cases
- 5. Examples
- 6. Conclusion
- References
- Chapter 21Ball Convergence Theorem forInexact Newton Methods inBanach Space
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- 4. Conclusion
- References
- Chapter 22Extending the Semi-LocalConvergence of a Stirling-TypeMethod
- 1. Introduction
- 2. Semi-Local Analysis
- References
- Chapter 23Newton's Method for Systems ofEquations with Constant RankDerivatives
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 24Extended Super-Halley Method
- 1. Introduction
- 2. Semi-Local Convergence
- References
- Chapter 25Chebyshev-Type Method ofOrder Three
- 1. Introduction
- 2. Convergence
- References
- Chapter 26Extended Semi-LocalConvergence of theChebyshev-Halley Method
- 1. Introduction
- 2. Convergence
- References
- Chapter 27Gauss-Newton-Type Schemesfor Undetermined Least SquaresProblems
- 1. Introduction
- 2. Semi-Local Convergence
- 3. Local Convergence
- References
- Glossary of Symbols
- About the Authors
- Index
- Blank Page
