Resolving the problem of multiple control parameters in optimized Borel-type summation

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-08-26 DOI:10.1007/s10910-024-01669-7

V. I. Yukalov, S. Gluzman

引用次数: 0

Abstract

One of the most often used methods of summing divergent series in physics is the Borel-type summation with control parameters improving convergence, which are defined by some optimization conditions. The well known annoying problem in this procedure is the occurrence of multiple solutions for control parameters. We suggest a method for resolving this problem, based on the minimization of cost functional. Control parameters can be introduced by employing the Borel–Leroy or Mittag–Leffler transforms. Also, two novel transformations are proposed using fractional integrals and fractional derivatives. New cost functionals are advanced, based on lasso and ridge selection criteria, and their performance is studied for a number of models. The developed method is shown to provide good accuracy for the calculated quantities.

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解决优化伯尔式求和中的多控制参数问题

物理学中最常用的发散级数求和方法之一是波尔型求和，其控制参数由一些优化条件确定，以提高收敛性。在这一过程中，众所周知的恼人问题是控制参数出现多解。我们提出了一种基于成本函数最小化的方法来解决这一问题。控制参数可以通过使用 Borel-Leroy 或 Mittag-Leffler 变换来引入。此外，还提出了使用分数积分和分数导数的两种新型变换。在套索和脊选择标准的基础上，提出了新的成本函数，并研究了它们在一些模型中的性能。结果表明，所开发的方法可为计算量提供良好的准确性。

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 Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.