{"title":"Calculation of a Multidimensional Integral with a Singularity by Dividing the Integration Domain into Subsegments","authors":"A. V. Friesen, D. Goderidze, Yu. L. Kalinovsky","doi":"10.1134/s1547477124701346","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Calculating multidimensional integrals with a singularity of type <span>\\(\\int \\ldots \\int {{{f(x)} \\mathord{\\left/ {\\vphantom {{f(x)} {\\left( {x - c} \\right)}}} \\right. \\kern-0em} {\\left( {x - c} \\right)}}} \\)</span> is not a simple task. The methods used to calculate such an integral must effectively bypass the singularity, minimizing the error. This work presents an algorithm that, in the process of calculating the integral, analyzes the area of integration, dividing it into subsegments. Subsegments containing a singularity, as well as those located close to the singularity, are excluded during the final calculation of the integral. Integrals final calulation is carried out using the Monte Carlo integration method. The algorithm allows to calculate both one-dimensional and multidimensional integrals.</p>","PeriodicalId":730,"journal":{"name":"Physics of Particles and Nuclei Letters","volume":"37 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Particles and Nuclei Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1547477124701346","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
Calculating multidimensional integrals with a singularity of type \(\int \ldots \int {{{f(x)} \mathord{\left/ {\vphantom {{f(x)} {\left( {x - c} \right)}}} \right. \kern-0em} {\left( {x - c} \right)}}} \) is not a simple task. The methods used to calculate such an integral must effectively bypass the singularity, minimizing the error. This work presents an algorithm that, in the process of calculating the integral, analyzes the area of integration, dividing it into subsegments. Subsegments containing a singularity, as well as those located close to the singularity, are excluded during the final calculation of the integral. Integrals final calulation is carried out using the Monte Carlo integration method. The algorithm allows to calculate both one-dimensional and multidimensional integrals.
AbstractCalculating multidimensional integrals with a singularity of type \(\int \ldots int {{{f(x)} \mathord \{left/ {\vphantom {{f(x)} {\left( {x - c} \right)}}}.\right.\kern-0em} {\left( {x -c} \right)}}\)并不是一项简单的任务。用于计算这种积分的方法必须有效地绕过奇点，使误差最小化。这项工作提出了一种算法，在计算积分的过程中，对积分区域进行分析，将其划分为若干子段。在积分的最终计算过程中，包含奇点的子段以及靠近奇点的子段将被排除在外。积分的最终计算采用蒙特卡罗积分法。该算法既可以计算一维积分，也可以计算多维积分。
期刊介绍：
The journal Physics of Particles and Nuclei Letters, brief name Particles and Nuclei Letters, publishes the articles with results of the original theoretical, experimental, scientific-technical, methodological and applied research. Subject matter of articles covers: theoretical physics, elementary particle physics, relativistic nuclear physics, nuclear physics and related problems in other branches of physics, neutron physics, condensed matter physics, physics and engineering at low temperatures, physics and engineering of accelerators, physical experimental instruments and methods, physical computation experiments, applied research in these branches of physics and radiology, ecology and nuclear medicine.
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