{"title":"Deslauriers-Dubuc插值尺度函数的小波伽辽金方法","authors":"N. Fukuda","doi":"10.21099/TKBJM/1389972032","DOIUrl":null,"url":null,"abstract":". Compactly supported orthonormal wavelets are often used in numerical analysis. However, since these functions have not an explicit formula in the time domain, the di‰culty of integrations often occurs. In this paper, we introduce the Galerkin method with Deslauriers–Dubuc interpolating scaling functions, and we use the biorthogonality of the wavelets to overcome the di‰culties of in-tegration. We present numerical results that show the e‰ciency and accuracy of this method.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"37 1","pages":"321-337"},"PeriodicalIF":0.3000,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the wavelet-Galerkin method with Deslauriers-Dubuc interpolating scaling functions\",\"authors\":\"N. Fukuda\",\"doi\":\"10.21099/TKBJM/1389972032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Compactly supported orthonormal wavelets are often used in numerical analysis. However, since these functions have not an explicit formula in the time domain, the di‰culty of integrations often occurs. In this paper, we introduce the Galerkin method with Deslauriers–Dubuc interpolating scaling functions, and we use the biorthogonality of the wavelets to overcome the di‰culties of in-tegration. We present numerical results that show the e‰ciency and accuracy of this method.\",\"PeriodicalId\":44321,\"journal\":{\"name\":\"Tsukuba Journal of Mathematics\",\"volume\":\"37 1\",\"pages\":\"321-337\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2013-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsukuba Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21099/TKBJM/1389972032\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/TKBJM/1389972032","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the wavelet-Galerkin method with Deslauriers-Dubuc interpolating scaling functions
. Compactly supported orthonormal wavelets are often used in numerical analysis. However, since these functions have not an explicit formula in the time domain, the di‰culty of integrations often occurs. In this paper, we introduce the Galerkin method with Deslauriers–Dubuc interpolating scaling functions, and we use the biorthogonality of the wavelets to overcome the di‰culties of in-tegration. We present numerical results that show the e‰ciency and accuracy of this method.
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