{"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}
引用次数: 0
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.
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.
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