Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume III

Name: Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume III
Brand: Nova Science Publishers Inc
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K. Argyros Ioannis(Author)

Nova Science Publishers Inc

Published on 20. September 2019

456 pages

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Intro
MATHEMATICAL MODELINGFOR THE SOLUTION OF EQUATIONSAND SYSTEMS OF EQUATIONS WITHAPPLICATIONSVOLUME III
MATHEMATICAL MODELINGFOR THE SOLUTION OF EQUATIONSAND SYSTEMS OF EQUATIONS WITHAPPLICATIONSVOLUME III
Contents
Preface
Chapter 1Local Convergence for a Family ofSuper-Halley Methods
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 2A Unified Local ConvergenceAnalysis of Newton-Like Methods
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
Conclusion
References
Chapter 3Ball Convergence Theorems forFourth-Order Variants of Newton'sMethod
1. Introduction
2. Local Convergence forMethod (3.3)
3. Numerical Examples
References
Chapter 4Local Convergence Theorems forSome Third and Fourth OrderMethods
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
Conclusion
References
Chapter 5Ball Convergence of Potra-Ptak-TypeMethod
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 6Householder-Type Iterative Freefrom Second Derivative
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 7Convergence for aNewton-Jarratt-Like Composition
1. Introduction
3. Numerical Examples
References
2. Local Convergence Analysis
Chapter 8Convergence for a Novel IterativeMethod Free From the SecondDerivative
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 9Ball Convergence Theorems forFourth-Order Variants of Newton'sMethod
1. Introduction
2. Local Convergence forMethod (9.3)
3. Numerical Examples
References
Chapter 10J. Chen's One Step Third-OrderIterative Methods
1. Introduction
2. Local Convergence forMethod (10.2)
3. Numerical Examples
References
Chapter 11Ball Convergence for a SixteenthOrder Iterative Methods
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 12Convergence for a Jarratt-LikeMethod for Solving Equations
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 13Convergence of a Sixth OrderOstrowski-Like Method for SolvingEquations
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 14Convergence for a Householder-LikeMethod
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 15Local Convergence of the Two-StepChebyshev-Like Method
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 16Comparison between Two SixthOrder Newton-Jarratt Method
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 17Newton's Method UsingGauss-Legendre Formulas
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 18Composite Newton-Traub Method
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 19Convergence of a Four Step NinthOrder Method
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 20Convergence of an Eighth-OrderMethod in Banach Space
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 21Convergence for a General Family ofOptimal Fourth-Order Methods
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 22Gauss-Newton Method UsingRestricted Convergence Domains
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 23Proximal Gauss-Newton MethodUsing Restricted ConvergenceDomains
1. Introduction
2. Background
3. Local Convergence Analysis of the Proximal Gauss-NewtonMethod
4. Numerical Examples
References
Chapter 24Hybrid High Convergence OrderIterative Methods
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 25High Convergence Order Methodson Riemannian Manifolds
1. Introduction
2. Semi-Local Convergence
3. IterativeMethods on a Sphere
3.1. Algorithm (Newton's Algorithm on the Sphere S2 [16])
References
Chapter 26Convergence Analysis of a M¨ullerSecant-Type Method
1. Introduction
2. Improved Convergence Ball Analysis of Method (26.4)
3. Local Convergence ofMethod (26.6)
4. Numerical Examples
References
Chapter 27Convergence of Bilinear Operator
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
References
Chapter 28Convergence Analysis forSemi-Smooth Newton-Type Methods
1. Introduction
2. Mathematical Background
3. Convergence Analysis I
4. Convergence Analysis II
References
Chapter 29Hybrid High Convergence OrderIterative Methods
1. Introduction
2. Convergence Analysis
3. Concluding Remarks and Applications
References
Chapter 30The King-Werner Method of Order1+p2
1. Introduction
2. Convergence Analysis of King-Werner-Type Methods (30.2)and (30.3)
3. Numerical Examples
References
Chapter 31Extending the Applicability ofKing-Werner-Type Methods
1. Introduction
2. Majorizing Sequences for King-Werner-TypeMethods (31.3)and (31.4)
3. Convergence Analysis of King-Werner-Type Methods (31.3)and (31.4)
4. Numerical Examples
References
Chapter 32Achieving Higher Order ofConvergence for Solving Systems ofEquations
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 33Gauss-Newton Method for ConvexComposite Optimization
1. Introduction
2. The Gauss-Newton Algorithm
2.1. Algorithm
2.2. Regularity
3. Semi-Local Convergence
4. Special Cases and Examples
References
Chapter 34High Order Method Based on theDecomposition Technique
1. Introduction
2. Local Convergence
3. Numerical Examples
References
Chapter 35Kantorovich-Type Extensions forNewton Method
1. Introduction
2. Semi-Local Convergence for Newton-Like Methods
3. Numerical Examples
References
Chapter 36Divided Difference Based IterativeMethods
1. Introduction
2. Local Convergence Analysis
3. Numerical Examples
References
Chapter 37Convergence for the Osada Method
1. Introduction
2. Auxiliary Results
3. Local Convergence
4. Numerical Examples
References
Chapter 38Convergence forNewton-Kantorovich-Like Theorems
1. Introduction
2. Background
3. Semilocal Convergence
References
Chapter 39Unified Convergence of FourthOrder Solvers
1. Introduction
2. Auxiliary Results
3. Ball Convergence
4. Numerical Examples
Conclusion
References
Chapter 40Extending the Kantorovich Theorem
1. Introduction
2. Convergence Analysis
3. Concluding Remarks and Applications
References
Chapter 41Two-Step Iterative Methods Free ofDerivatives
1. Introduction
2. Local Convergence I
3. Local Convergence II
4. Numerical Examples
References
Chapter 42Inexact Newton-Type Methods
1. Introduction
2. Local Convergence Analysis of INTM
3. Numerical Example
References
About the Authors
Index
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Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume III

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