{"title":"正则区域上基于欧拉求和的培养的Romberg外推。","authors":"W Freeden, C Gerhards","doi":"10.1007/s13137-017-0097-4","DOIUrl":null,"url":null,"abstract":"<p><p>Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in <i>q</i> dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary <i>q</i>-dimensional regular regions [Formula: see text] and derive an explicit representation for the remainder term.</p>","PeriodicalId":44484,"journal":{"name":"GEM-International Journal on Geomathematics","volume":"8 2","pages":"169-182"},"PeriodicalIF":1.9000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s13137-017-0097-4","citationCount":"2","resultStr":"{\"title\":\"Romberg extrapolation for Euler summation-based cubature on regular regions.\",\"authors\":\"W Freeden, C Gerhards\",\"doi\":\"10.1007/s13137-017-0097-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in <i>q</i> dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary <i>q</i>-dimensional regular regions [Formula: see text] and derive an explicit representation for the remainder term.</p>\",\"PeriodicalId\":44484,\"journal\":{\"name\":\"GEM-International Journal on Geomathematics\",\"volume\":\"8 2\",\"pages\":\"169-182\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s13137-017-0097-4\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"GEM-International Journal on Geomathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13137-017-0097-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2017/9/11 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"GEM-International Journal on Geomathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13137-017-0097-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2017/9/11 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Romberg extrapolation for Euler summation-based cubature on regular regions.
Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in q dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary q-dimensional regular regions [Formula: see text] and derive an explicit representation for the remainder term.
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