斐波那契格点的积分与逼近

IF 0.6 Q3 MATHEMATICS

Dolomites Research Notes on Approximation Pub Date : 2015-12-01 DOI:10.14658/PUPJ-DRNA-2015-SPECIAL_ISSUE-9

G. Suryanarayana, R. Cools, Dirk Nuyens

{"title":"斐波那契格点的积分与逼近","authors":"G. Suryanarayana, R. Cools, Dirk Nuyens","doi":"10.14658/PUPJ-DRNA-2015-SPECIAL_ISSUE-9","DOIUrl":null,"url":null,"abstract":"We study the properties of a special rank-1 point set in 2 dimensions — Fibonacci lattice points. We present the analysis of these point sets for cubature and approximation of bivariate periodic functions with decaying spectral coefficients. We are interested in truncating the frequency space into index sets based on different degrees of exactness. The numerical results support that the Lebesgue constant of these point sets grows like the conjectured optimal rate ln 2 (N), where N is the number of sample points.","PeriodicalId":51943,"journal":{"name":"Dolomites Research Notes on Approximation","volume":"8 1","pages":"92-101"},"PeriodicalIF":0.6000,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integration and Approximation with Fibonacci lattice points\",\"authors\":\"G. Suryanarayana, R. Cools, Dirk Nuyens\",\"doi\":\"10.14658/PUPJ-DRNA-2015-SPECIAL_ISSUE-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the properties of a special rank-1 point set in 2 dimensions — Fibonacci lattice points. We present the analysis of these point sets for cubature and approximation of bivariate periodic functions with decaying spectral coefficients. We are interested in truncating the frequency space into index sets based on different degrees of exactness. The numerical results support that the Lebesgue constant of these point sets grows like the conjectured optimal rate ln 2 (N), where N is the number of sample points.\",\"PeriodicalId\":51943,\"journal\":{\"name\":\"Dolomites Research Notes on Approximation\",\"volume\":\"8 1\",\"pages\":\"92-101\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2015-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dolomites Research Notes on Approximation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14658/PUPJ-DRNA-2015-SPECIAL_ISSUE-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dolomites Research Notes on Approximation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14658/PUPJ-DRNA-2015-SPECIAL_ISSUE-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

研究了二维空间中一类特殊的秩1点集-斐波那契格点的性质。我们给出了这些点集的分析，用于建立和逼近具有衰减谱系数的二元周期函数。我们感兴趣的是将频率空间截断成基于不同精确度的索引集。数值结果支持这些点集的Lebesgue常数以推测的最优速率ln 2 (N)增长，其中N为样本点的个数。

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

Integration and Approximation with Fibonacci lattice points

We study the properties of a special rank-1 point set in 2 dimensions — Fibonacci lattice points. We present the analysis of these point sets for cubature and approximation of bivariate periodic functions with decaying spectral coefficients. We are interested in truncating the frequency space into index sets based on different degrees of exactness. The numerical results support that the Lebesgue constant of these point sets grows like the conjectured optimal rate ln 2 (N), where N is the number of sample points.

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

Dolomites Research Notes on Approximation MATHEMATICS-

CiteScore

1.70

自引率

7.70%

发文量

审稿时长

8 weeks

期刊介绍： Dolomites Research Notes on Approximation is an open access journal that publishes peer-reviewed papers. It also publishes lecture notes and slides of the tutorials presented at the annual Dolomites Research Weeks and Workshops, which have been organized regularly since 2006 by the Padova-Verona Research Group on Constructive Approximation and Applications (CAA) in Alba di Canazei (Trento, Italy). The journal publishes, on invitation, survey papers and summaries of Ph.D. theses on approximation theory, algorithms, and applications.