Fractional Newton-Raphson Method Accelerated with Aitken's Method
| Autor: | A. Torres-Hernandez, Reyna Caballero-Cruz, F. Brambila-Paz, Ursula Iturrarán-Viveros |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Logic
Iterative method 010103 numerical & computational mathematics 02 engineering and technology Derivative fractional calculus 01 natural sciences symbols.namesake Simple (abstract algebra) Convergence (routing) FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Order (group theory) Applied mathematics Mathematics - Numerical Analysis Complex Variables (math.CV) 0101 mathematics Newton's method Mathematical Physics Mathematics Algebra and Number Theory Mathematics - Complex Variables lcsh:Mathematics fractional derivative Numerical Analysis (math.NA) lcsh:QA1-939 Fractional calculus Rate of convergence symbols 020201 artificial intelligence & image processing Geometry and Topology Newton–Raphson method Analysis Aitken’s method |
| Zdroj: | Axioms Volume 10 Issue 2 Axioms, Vol 10, Iss 47, p 47 (2021) |
| Popis: | In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the derivative is different from one. A simplified way of constructing the Riemann-Liouville (R-L) fractional operators, fractional integral and fractional derivative, is presented along with examples of its application on different functions. Furthermore, an introduction to the Aitken's method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, to finally present the results that were obtained when implementing the Aitken's method in the F N-R method. Comment: Newton-Raphson Method, Fractional Calculus, Fractional Derivative of Riemann-Liouville, Method of Aitken. arXiv admin note: substantial text overlap with arXiv:1710.07634 |
| Databáze: | OpenAIRE |
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