{"title":"一个快速构造带限函数的正交公式的程序","authors":"A. Gopal , V. Rokhlin","doi":"10.1016/j.acha.2023.05.001","DOIUrl":null,"url":null,"abstract":"<div><p><span>We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate </span><span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> to construct an <em>n</em>-point quadrature rule. Moreover, the size of the “<span><math><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi></math></span>” term in the CPU time estimate is small, so for all practical purposes the CPU time cost is proportional to <em>n</em>. The performance of the algorithm is illustrated by several numerical examples.</p></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"66 ","pages":"Pages 193-210"},"PeriodicalIF":2.6000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A fast procedure for the construction of quadrature formulas for bandlimited functions\",\"authors\":\"A. Gopal , V. Rokhlin\",\"doi\":\"10.1016/j.acha.2023.05.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate </span><span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> to construct an <em>n</em>-point quadrature rule. Moreover, the size of the “<span><math><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi></math></span>” term in the CPU time estimate is small, so for all practical purposes the CPU time cost is proportional to <em>n</em>. The performance of the algorithm is illustrated by several numerical examples.</p></div>\",\"PeriodicalId\":55504,\"journal\":{\"name\":\"Applied and Computational Harmonic Analysis\",\"volume\":\"66 \",\"pages\":\"Pages 193-210\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Harmonic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S106352032300043X\",\"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 and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S106352032300043X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A fast procedure for the construction of quadrature formulas for bandlimited functions
We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate to construct an n-point quadrature rule. Moreover, the size of the “” term in the CPU time estimate is small, so for all practical purposes the CPU time cost is proportional to n. The performance of the algorithm is illustrated by several numerical examples.
期刊介绍：
Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.
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