广义多步Steffensen迭代法。求解光电倍增管器件的模型

IF 1.7 4区 数学 Q2 MATHEMATICS, APPLIED
Eva G. Villalba, J. L. Hueso, E. Martínez
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引用次数: 0

摘要

众所周知,steffensen型方法是用一阶差分分算子逼近牛顿格式中的导数。广义多步Steffensen迭代法是将该方法与自身组合m次。具体来说,在更新之前,每m步的分割差保持不变。在本文中,我们对该方法进行了改进,以加快收敛速度。在该方案中,我们计算第一步和第二步的除差,并在接下来的m−1步中使用第二步的除差。我们对该方案的计算效率进行了详尽的研究,并将内存引入该方法以加快收敛速度,而无需执行新的功能评估。最后,通过数值算例验证了算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generalized multistep Steffensen iterative method. Solving the model of a photomultiplier device
It is well known that the Steffensen-type methods approximate the derivative appearing in Newton's scheme by means of the first-order divided difference operator. The generalized multistep Steffensen iterative method consists of composing the method with itself m times. Specifically, the divided difference is held constant for every m steps before it is updated. In this work, we introduce a modification to this method, in order to accelerate the convergence order. In the proposed, scheme we compute the divided differences in first and second step and use the divided difference from the second step in the following m−1 steps. We perform an exhaustive study of the computational efficiency of this scheme and also introduce memory to this method to speed up convergence without performing new functional evaluations. Finally, some numerical examples are studied to verify the usefulness of these algorithms.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
72
审稿时长
5 months
期刊介绍: International Journal of Computer Mathematics (IJCM) is a world-leading journal serving the community of researchers in numerical analysis and scientific computing from academia to industry. IJCM publishes original research papers of high scientific value in fields of computational mathematics with profound applications to science and engineering. IJCM welcomes papers on the analysis and applications of innovative computational strategies as well as those with rigorous explorations of cutting-edge techniques and concerns in computational mathematics. Topics IJCM considers include: • Numerical solutions of systems of partial differential equations • Numerical solution of systems or of multi-dimensional partial differential equations • Theory and computations of nonlocal modelling and fractional partial differential equations • Novel multi-scale modelling and computational strategies • Parallel computations • Numerical optimization and controls • Imaging algorithms and vision configurations • Computational stochastic processes and inverse problems • Stochastic partial differential equations, Monte Carlo simulations and uncertainty quantification • Computational finance and applications • Highly vibrant and robust algorithms, and applications in modern industries, including but not limited to multi-physics, economics and biomedicine. Papers discussing only variations or combinations of existing methods without significant new computational properties or analysis are not of interest to IJCM. Please note that research in the development of computer systems and theory of computing are not suitable for submission to IJCM. Please instead consider International Journal of Computer Mathematics: Computer Systems Theory (IJCM: CST) for your manuscript. Please note that any papers submitted relating to these fields will be transferred to IJCM:CST. Please ensure you submit your paper to the correct journal to save time reviewing and processing your work. Papers developed from Conference Proceedings Please note that papers developed from conference proceedings or previously published work must contain at least 40% new material and significantly extend or improve upon earlier research in order to be considered for IJCM.
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