任意次有理数算子族的动力学

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2021-05-26 DOI:10.3846/mma.2021.12642

B. Campos, Jordi Canela, A. Garijo, P. Vindel

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引用次数: 1

摘要

本文分析了一类四阶寻根算法的有理数算子族的动力学性质。我们首先证明了重新定义参数可以方便地防止问题参数的冗余和无界性。在重新参数化之后，我们观察到这些有理映射属于一个更一般的n+k次算子族Oa,n,k，它包含了其他数值方法得到的映射族。我们研究了Oa,n,k的动力学，并从数值的角度讨论了n和k这些算子适合于哪些参数。

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Dynamics of a family of rational operators of Arbitrary degree

In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and unboundedness of problematic parameters. After reparametrization, we observe that these rational maps belong to a more general family Oa,n,k of degree n+k operators, which includes several other families of maps obtained from other numerical methods. We study the dynamics of Oa,n,k and discuss for which parameters n and k these operators would be suitable from the numerical point of view.

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