{"title":"博尔赫斯意义下最优正交规则集的构造","authors":"A. Jovanovic, M. Stanić, Tatjana V. Tomovic","doi":"10.1553/ETNA_VOL50S164","DOIUrl":null,"url":null,"abstract":"Abstract. In this paper we give a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges [Numer. Math., 67 (1994), pp. 271–288] for definite integrals with the same integrand and interval of integration but with different weight functions related to an arbitrary multi-index. We present a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges for four weight functions and explain how to perform an analogous construction for an arbitrary number of weight functions.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Construction of the optimal set of quadrature rules in the sense of Borges\",\"authors\":\"A. Jovanovic, M. Stanić, Tatjana V. Tomovic\",\"doi\":\"10.1553/ETNA_VOL50S164\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. In this paper we give a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges [Numer. Math., 67 (1994), pp. 271–288] for definite integrals with the same integrand and interval of integration but with different weight functions related to an arbitrary multi-index. We present a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges for four weight functions and explain how to perform an analogous construction for an arbitrary number of weight functions.\",\"PeriodicalId\":282695,\"journal\":{\"name\":\"ETNA - Electronic Transactions on Numerical Analysis\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ETNA - Electronic Transactions on Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1553/ETNA_VOL50S164\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ETNA - Electronic Transactions on Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1553/ETNA_VOL50S164","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
摘要本文给出了在博尔赫斯数意义上构造最优正交规则集的一种数值方法。数学。对于具有相同被积和积分区间但与任意多指标相关的不同权函数的定积分，[j]， 67 (1994)， pp. 271-288]。本文给出了一种构造四个权函数在博尔赫斯意义上的最优正交规则集的数值方法，并解释了如何对任意数量的权函数进行类似的构造。
Construction of the optimal set of quadrature rules in the sense of Borges
Abstract. In this paper we give a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges [Numer. Math., 67 (1994), pp. 271–288] for definite integrals with the same integrand and interval of integration but with different weight functions related to an arbitrary multi-index. We present a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges for four weight functions and explain how to perform an analogous construction for an arbitrary number of weight functions.
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