Enhancing the applicability of Chebyshev-like method

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-04-17 DOI:10.1016/j.jco.2024.101854

Santhosh George, Indra Bate, Muniyasamy M, Chandhini G, Kedarnath Senapati

引用次数: 0

Abstract

Ezquerro and Hernandez (2009) studied a modified Chebyshev's method to solve a nonlinear equation approximately in the Banach space setting where the convergence analysis utilizes Taylor series expansion and hence requires the existence of at least fourth-order Fréchet derivative of the involved operator. No error estimate on the error distance was given in their work. In this paper, we obtained the convergence order and error estimate of the error distance without Taylor series expansion. We have made assumptions only on the involved operator and its first and second Fréchet derivative. So, we extend the applicability of the modified Chebyshev's method. Further, we compare the modified Chebyshev method's efficiency index and dynamics with other similar methods. Numerical examples validate the theoretical results.

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增强类切比雪夫方法的适用性

Ezquerro 和 Hernandez（2009 年）研究了一种改进的切比雪夫方法，用于近似求解巴拿赫空间环境下的非线性方程，其中的收敛分析利用了泰勒级数展开，因此要求至少存在相关算子的四阶弗雷谢特导数。他们的研究没有给出误差距离的误差估计。在本文中，我们在不使用泰勒级数展开的情况下获得了误差距离的收敛阶次和误差估计。我们只对所涉及的算子及其第一次和第二次弗雷谢特导数作了假设。因此，我们扩展了修正的切比雪夫方法的适用范围。此外，我们还将修正的切比雪夫方法的效率指数和动力学特性与其他类似方法进行了比较。数值实例验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.