基于逆有理插值的新一族寻根算法

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI:10.2298/aadm220708003d

J. Dzunic

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引用次数: 0

摘要

研究了用有理函数进行逆插值的方法，用于根近似的迭代求精。提出了求解非线性方程的一类新的任意大阶收敛最优方法。通过实验验证了分子和分母的多项式度对所提方法收敛性的影响。由于Wolfram Mathematica 12软件具有任意大精度运算的能力，因此采用该软件进行计算。

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New family of root-finding algorithms based on inverse rational interpolation

Inverse interpolation with rational functions is investigated for the use in iterative refinement of the root approximation. A new family of optimal methods of arbitrary large order of convergence for solving nonlinear equations is presented. Experiments are conducted to check the influence of polynomial degrees in numerator and denominator on convergence properties of the proposed methods. Wolfram Mathematica 12 software was used to carry the computation due to its capabilities of arbitrary large precision arithmetic.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).