
Contemporary Algorithms for Solving Problems in Economics and Other Disciplines
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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
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