{"title":"On the Approximability and Curse of Dimensionality of Certain Classes of High-Dimensional Functions","authors":"Christian Rieger, Holger Wendland","doi":"10.1137/22m1525193","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 842-871, April 2024. <br/> Abstract. In this paper, we study the approximability of high-dimensional functions that appear, for example, in the context of many body expansions and high-dimensional model representation. Such functions, though high-dimensional, can be represented as finite sums of lower-dimensional functions. We will derive sampling inequalities for such functions, give explicit advice on the location of good sampling points, and show that such functions do not suffer from the curse of dimensionality.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"57 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1525193","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
Abstract
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 842-871, April 2024. Abstract. In this paper, we study the approximability of high-dimensional functions that appear, for example, in the context of many body expansions and high-dimensional model representation. Such functions, though high-dimensional, can be represented as finite sums of lower-dimensional functions. We will derive sampling inequalities for such functions, give explicit advice on the location of good sampling points, and show that such functions do not suffer from the curse of dimensionality.
期刊介绍：
SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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