单位插值有理RBF分割中形状参数的优化

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-19 DOI:10.1016/j.aml.2025.109766

Roberto Cavoretto

{"title":"单位插值有理RBF分割中形状参数的优化","authors":"Roberto Cavoretto","doi":"10.1016/j.aml.2025.109766","DOIUrl":null,"url":null,"abstract":"<div><div>In this article we enhance the rational RBF partition of unity (RBF-PU) method presented in Farazandeh and Mirzaei (2021) for shape parameter free RBFs. Here, we propose a leave-one-out cross-validation technique to optimize the RBF shape parameter in the context of rational interpolation. This approach enables us to obtain remarkable results in the rational RBF-PU scheme for shape parameter dependent RBFs. Numerical experiments highlight performance of the rational RBF-PU interpolation, also in comparison to that of the standard method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109766"},"PeriodicalIF":2.8000,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimizing the shape parameter in rational RBF partition of unity interpolation\",\"authors\":\"Roberto Cavoretto\",\"doi\":\"10.1016/j.aml.2025.109766\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this article we enhance the rational RBF partition of unity (RBF-PU) method presented in Farazandeh and Mirzaei (2021) for shape parameter free RBFs. Here, we propose a leave-one-out cross-validation technique to optimize the RBF shape parameter in the context of rational interpolation. This approach enables us to obtain remarkable results in the rational RBF-PU scheme for shape parameter dependent RBFs. Numerical experiments highlight performance of the rational RBF-PU interpolation, also in comparison to that of the standard method.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"173 \",\"pages\":\"Article 109766\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965925003167\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925003167","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们增强了Farazandeh和Mirzaei（2021）提出的用于无形状参数RBF的有理RBF划分统一（RBF- pu）方法。在此，我们提出了一种留一交叉验证技术来优化RBF形状参数在有理插值的背景下。这种方法使我们在形状参数相关的RBF-PU方案中获得了显著的结果。数值实验显示了合理的RBF-PU插值方法的性能，并与标准方法进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Optimizing the shape parameter in rational RBF partition of unity interpolation

In this article we enhance the rational RBF partition of unity (RBF-PU) method presented in Farazandeh and Mirzaei (2021) for shape parameter free RBFs. Here, we propose a leave-one-out cross-validation technique to optimize the RBF shape parameter in the context of rational interpolation. This approach enables us to obtain remarkable results in the rational RBF-PU scheme for shape parameter dependent RBFs. Numerical experiments highlight performance of the rational RBF-PU interpolation, also in comparison to that of the standard method.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.