{"title":"关于多变量函数的近似","authors":"B. Mond, O. Shisha","doi":"10.6028/JRES.070B.019","DOIUrl":null,"url":null,"abstract":"1. The purpose of this note is to point out how a certain type of approximation to fun ctions of one real variable, gives rise to similar approximations to functions of several variables. In fact, we show how information on the rapidity of cOQvergence of the approximation in the one dimensional case, yields at once corresponding information for the multidimensional case. 2. Let -oo < a < b <oo, and for n=l, 2, . .. , let c~,), cln), . •• , c\\!') be points of [a, b], and Kbn)(X), K\\n)(x), ... , K~n)(x) polynomials which are ;;:z,: ° throughout [a , b], and such that","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1966-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"On the approximation of functions of several variables\",\"authors\":\"B. Mond, O. Shisha\",\"doi\":\"10.6028/JRES.070B.019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"1. The purpose of this note is to point out how a certain type of approximation to fun ctions of one real variable, gives rise to similar approximations to functions of several variables. In fact, we show how information on the rapidity of cOQvergence of the approximation in the one dimensional case, yields at once corresponding information for the multidimensional case. 2. Let -oo < a < b <oo, and for n=l, 2, . .. , let c~,), cln), . •• , c\\\\!') be points of [a, b], and Kbn)(X), K\\\\n)(x), ... , K~n)(x) polynomials which are ;;:z,: ° throughout [a , b], and such that\",\"PeriodicalId\":408709,\"journal\":{\"name\":\"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics\",\"volume\":\"32 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1966-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6028/JRES.070B.019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/JRES.070B.019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
摘要
1. 这篇笔记的目的是指出,对一个真实变量的有趣函数的某种近似如何产生对多个变量函数的类似近似。事实上,我们展示了一维情况下近似的coq收敛速度的信息如何立即产生多维情况下的相应信息。2. 令-oo < a < b 本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the approximation of functions of several variables
1. The purpose of this note is to point out how a certain type of approximation to fun ctions of one real variable, gives rise to similar approximations to functions of several variables. In fact, we show how information on the rapidity of cOQvergence of the approximation in the one dimensional case, yields at once corresponding information for the multidimensional case. 2. Let -oo < a < b