In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function.
Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
Author(s): George A. Anastassiou, Ioannis K. Argyros
Series: Studies in Computational Intelligence
Publisher: Springer
Year: 2016
Language: English
Pages: 427
Tags: Computational Intelligence; Artificial Intelligence (incl. Robotics); Computational Science and Engineering; Complexity
Front Matter....Pages i-xvi
Newton-Like Methods on Generalized Banach Spaces and Fractional Calculus....Pages 1-21
Semilocal Convegence of Newton-Like Methods and Fractional Calculus....Pages 23-37
Convergence of Iterative Methods and Generalized Fractional Calculus....Pages 39-56
Fixed Point Techniques and Generalized Right Fractional Calculus....Pages 57-74
Approximating Fixed Points and k-Fractional Calculus....Pages 75-93
Iterative Methods and Generalized g-Fractional Calculus....Pages 95-106
Unified Convergence Analysis for Iterative Algorithms and Fractional Calculus....Pages 107-125
Convergence Analysis for Extended Iterative Algorithms and Fractional and Vector Calculus....Pages 127-147
Convergence Analysis for Extended Iterative Algorithms and Fractional Calculus....Pages 149-162
Secant-Like Methods and Fractional Calculus....Pages 163-175
Secant-Like Methods and Modified g-Fractional Calculus....Pages 177-196
Secant-Like Algorithms and Generalized Fractional Calculus....Pages 197-214
Secant-Like Methods and Generalized g-Fractional Calculus of Canavati-Type....Pages 215-230
Iterative Algorithms and Left-Right Caputo Fractional Derivatives....Pages 231-243
Iterative Methods on Banach Spaces with a Convergence Structure and Fractional Calculus....Pages 245-262
Inexact Gauss-Newton Method for Singular Equations....Pages 263-281
The Asymptotic Mesh Independence Principle....Pages 283-296
Ball Convergence of a Sixth Order Iterative Method....Pages 297-307
Broyden’s Method with Regularly Continuous Divided Differences....Pages 309-316
Left General Fractional Monotone Approximation....Pages 317-335
Right General Fractional Monotone Approximation Theory....Pages 337-352
Left Generalized High Order Fractional Monotone Approximation....Pages 353-372
Right Generalized High Order Fractional Monotone Approximation....Pages 373-389
Advanced Fractional Taylor’s Formulae....Pages 391-412
Generalized Canavati Type Fractional Taylor’s Formulae....Pages 413-420
Back Matter....Pages 421-423
