The Fibonacci family of iterative processes for solving nonlinear equations
| Autor: | Ariel Sapir, Tamara Kogan, Luba Sapir, Amir Sapir |
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| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Class (set theory) Mathematical optimization Fibonacci number Iterative method Applied Mathematics 010102 general mathematics 020206 networking & telecommunications 02 engineering and technology 01 natural sciences Local convergence Computational Mathematics Nonlinear system Rate of convergence Secant method Convergence (routing) 0202 electrical engineering electronic engineering information engineering Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Applied Numerical Mathematics. 110:148-158 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2016.08.012 |
| Popis: | This paper presents a class of stationary iterative processes with convergence order equal to the growth rate of generalized Fibonacci sequences. We prove that the informational and computational efficiency of the processes of our class tends to 2 from below.The paper illustrates a connection of the methods of the class with the nonstationary iterative method suggested by our previous paper, whose efficiency index equals to 2. We prove that the efficiency of the nonstationary iterative method, measured by Ostrowski-Traub criteria, is maximal among all iterative processes of order 2. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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