The book provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational Sciences, Engineering, Scientific Computing and Medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms which are universally applicable is presented on a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of Analysis, Linear Algebra and some Computing experience is required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems.
Author(s): Christopher I. Argyros, Samundra Regmi, Ioannis K. Argyros
Publisher: Nova Science Publishers
Year: 2023
Language: English
Pages: 442
Contemporary AlgorithmsTheory and ApplicationsVolume III
Contents
Preface
Chapter 1Local Convergence for a Two-StepThird Order Secant-Like Methodwithout Bilinear Operators
1. Introduction
2. Convergence
Bibliograohy
Chapter 2Semi-Local Convergence for aDerivative Free Method with ErrorControlled Controlled Iterates forSolving Nonlinear Equations
1. Introduction
2. Convergence of Majorizing Sequences
3. Convergence of Method (2.2)
Bibliography
Chapter 3On the Semi-Local Convergence of aSharma-Gupta Fifth Order Methodfor Solving Nonlinear Equations
1. Introduction
2. Convergence
Bibliography
Chapter 4On the Semi-Local Convergence of aSeventh Order Method for NonlinearEquations Convergence for a SeventhOrder Method for Equations
1. Introduction
2. Semi-Local Convergence
Bibliography
Chapter 5On the Semi-Local Convergence of aFifth Order Method for SolvingNonlinear Equations
1. Introduction
2. Sequences Majorizing Method (5.2)
3. Analysis for Method ( 5.2)
Bibliography
Chapter 6On the Semi-Local Convergence of aFifth Order Efficient Method forSolving Nonlinear Equations
1. Introduction
2. Semi-Local Analysis
Bibliography
Chapter 7Improved Convergence ofDerivative-Free Halley’s Schemewith Two Parameters
1. Introduction
2. Semi-Local Convergence I
3. Semi-Local Convergence Part 2
Bibliography
Chapter 8Extended Convergence for a ThirdOrder Traub-Like Method withParameter for Solving Equations
1. Introduction
2. Majorizing Sequence
3. Convergence of Method (8.3)
4. Numerical Experiments
Bibliography
Chapter 9Ball Convergence Comparison forMethods Whose First Step is Givenby Newton’s for Solving NonlinearEquations
1. Introduction
2. Ball Convergence
Bibliography
Chapter 10Extending the Convergence of aSteffensen-Like Method withoutDerivatives for Solving NonlinearEquations
1. Introduction
2. Majorizing Sequences
Bibliography
Chapter 11On the Semi-Local Convergence of aFourth Order Derivative FreeTwo-Step Steffensen Method forSolving Equations
1. Introduction
2. Majorizing Sequences
3. Convergence for Method (11.2)
Bibliography
Chapter 12A Semi-Local Convergence for aClass of Fourth Order Method forSolving Equations
1. Introduction
2. Semi-Local Convergence
Bibliography
Chapter 13Local Convergence Comparisonbetween Two Competing Fifth OrderIterations
1. Introduction
2. Real Majorizing Function
3. Local Analysis
Bibliography
Chapter 14Semi-Local Convergence Analysis ofHigh Convergence Order Iterationsunder the Same Set of Conditions
1. Introduction
2. Semi-Local Analysis
3. Numerical Example
Bibliography
Chapter 15A Collection of Iterative Methodswith Order Five, Six and Seven andTheir Semi-Local Convergence
1. Introduction
2. Convergence Criteria
Bibliography
Chapter 16Extended Semi-Local ConvergenceAnalysis for the Two-Step NewtonMethod under Generalized LipschitzConditions
1. Introduction
2. Semi-Local Convergence
Bibliography
Chapter 17Semi-Local Convergence forJarratt-Like Methods underGeneralized Conditions for SolvingEquations
1. Introduction
2. SL ofMethod (17.3) and Method (17.2)
Bibliography
Chapter 18On the Semi-Local Convergence of aDerivative Free Fourth OrderMethod for Solving Equations
1. Introduction
2. Majorizing Sequence
3. Semi-Local Convergence
Bibliography
Chapter 19Extended and Unified KantorovichTheory for Solving GeneralizedNonlinear Equations
1. Introduction
2. Mathematical Background
3. Majorizing Sequence
4. Main Result
Bibliography
Chapter 20A Derivative Free Two-Step FourthOrder Method for Solving Equationsin Banach Space
1. Introduction
2. Local Convergence Analysis
Bibliography
Chapter 21Local Convergence for an EfficientDerivative Free Fourth OrderMethod for Solving Equations inBanach Space
1. Introduction
2. Convergence
Bibliography
Chapter 22Extended Local Convergence ofSteffensen-Type Methods for SolvingNonlinear Equations in BanachSpace
1. Introduction
2. Local Analysis of STM
Bibliography
Chapter 23Extended Convergence Analysis ofOptimal Eighth Order Methods forSolving Nonlinear Equations inBanach Space
1. Introduction
2. Local Convergence
3. Special Cases
Bibliography
Chapter 24Efficient Fifth Convergence OrderMethods for Solving Equations inBanach Space
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
Bibliography
Chapter 25Efficient Derivative Free SeventhOrder Methods for SolvingEquations in Banach Space
1. Introduction
2. Convergence for Method (25.4)
3. Special Cases
4. Convergence of Method (25.7)
Bibliography
Chapter 26Necessary and Sufficient Conditionsfor the Q-Order of Convergence ofIterative Methods
1. Introduction
2. Local Convergence
Bibliography
Chapter 27Necessary and Sufficient Conditionsfor the Convergence of Sixth Orderor Higher Derivative Free Methods
1. Introduction
2. Local Convergence
Bibliography
Chapter 28The Convergence Analysis of SomeFourth and Fifth Order Methods
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
Bibliography
Chapter 29High Convergence Order DerivativeFree Methods-I
1. Introduction
2. Local Convergence Analysis
3. Semi-Local Convergence
Bibliography
Chapter 30High Convergence Order DerivativeFree Methods-II
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
Bibliography
Chapter 31High Convergence Order DerivativeFree Methods-III
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
Bibliography
Chapter 32Fourth Convergence OrderDerivative Free Methods with orwithout Memory
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
Bibliography
Chapter 33Convergence Radius of an EfficientIterative Method with FrozenDerivatives
1. Introduction
2. Convergence for Method (33.2)
3. Numerical Examples
Bibliography
Chapter 34A Comparison between SomeDerivative Free Methods
1. Introduction
2. Local Convergence
Bibliography
Chapter 35High Convergence Order Methods
1. Introduction
2. Semi-Local Convergence
Bibliography
Chapter 36On a Family of Optimal EighthOrder Methods for Equations inBanach Space
1. Introduction
2. Local Analysis
Bibliography
Chapter 37Extended Ball Convergence of aXiao-Yin Fifth Order Scheme forEquations
1. Introduction
2. Ball Convergence
3. Numerical Experiments
Bibliography
Chapter 38On the Semi-Local Convergence ofKing’s Fourth Order Method forSolving Equations
1. Introduction
2. Scalar Majorizing Sequences
3. Analysis
4. Convergence Result for Method 38.3
5. Applications
Bibliography
Chapter 39On the Convergence of Two EighthOrder Methods with DividedDifferences and Derivatives
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
Bibliography
Chapter 40Bilinear Operator Free Method forSolving Nonlinear Equations
1. Introduction
2. History of the Procedure
3. Convergence Analysis
4. Numerical Experiments
Bibliography
Index
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