局部 C2 平滑样条准插值法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-10-26 DOI:10.1016/j.aml.2024.109346

D. Barrera , S. Eddargani , M.J. Ibáñez , S. Remogna

{"title":"局部 C2 平滑样条准插值法","authors":"D. Barrera , S. Eddargani , M.J. Ibáñez , S. Remogna","doi":"10.1016/j.aml.2024.109346","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we construct new univariate local <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> quasi-interpolating splines having specific polynomial reproduction properties. The splines are directly determined by setting their Bernstein-Bézier coefficients to appropriate combinations of the given data values. In certain cases we obtain a family of quasi-interpolating operators satisfying the required conditions, so we fix some extra properties (interpolation of the vertices, extra locality, extra polynomial reproduction) in order to compute unique approximants. We also provide numerical results confirming the theoretical ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109346"},"PeriodicalIF":2.9000,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local C2-smooth spline quasi-interpolation methods\",\"authors\":\"D. Barrera , S. Eddargani , M.J. Ibáñez , S. Remogna\",\"doi\":\"10.1016/j.aml.2024.109346\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper we construct new univariate local <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> quasi-interpolating splines having specific polynomial reproduction properties. The splines are directly determined by setting their Bernstein-Bézier coefficients to appropriate combinations of the given data values. In certain cases we obtain a family of quasi-interpolating operators satisfying the required conditions, so we fix some extra properties (interpolation of the vertices, extra locality, extra polynomial reproduction) in order to compute unique approximants. We also provide numerical results confirming the theoretical ones.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"160 \",\"pages\":\"Article 109346\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-10-26\",\"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/S0893965924003665\",\"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/S0893965924003665","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，我们构建了具有特定多项式再现特性的新的单变量局部 C2 准插值样条。通过将其 Bernstein-Bézier 系数设置为给定数据值的适当组合，可以直接确定这些样条。在某些情况下，我们会得到满足所需条件的准插值算子族，因此我们会固定一些额外的属性（顶点插值、额外的局部性、额外的多项式再现），以便计算唯一的近似值。我们还提供了证实理论结果的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Local C2-smooth spline quasi-interpolation methods

In this paper we construct new univariate local

C^{2}

quasi-interpolating splines having specific polynomial reproduction properties. The splines are directly determined by setting their Bernstein-Bézier coefficients to appropriate combinations of the given data values. In certain cases we obtain a family of quasi-interpolating operators satisfying the required conditions, so we fix some extra properties (interpolation of the vertices, extra locality, extra polynomial reproduction) in order to compute unique approximants. We also provide numerical results confirming the theoretical ones.

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.