基于逆有理插值的新一族寻根算法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.