Contemporary Algorithms for Solving Problems in Economics and Other Disciplines
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 cl...
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| Médium: | E-kniha |
| Jazyk: | English |
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New York
Nova Science Publishers, Incorporated
2020
Nova Science |
| Vydanie: | 1 |
| Edícia: | Mathematics Research Developments |
| Predmet: | |
| ISBN: | 1536181285, 9781536181289 |
| On-line prístup: | Získať plný text |
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- 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