{"title":"切比雪夫近似多变量函数的有理表达式与插值","authors":"P. Malachivskyy, L. Melnychok, Y. Pizyur","doi":"10.17721/2706-9699.2022.2.09","DOIUrl":null,"url":null,"abstract":"A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p \\to \\infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"41 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"CHEBYSHEV APPROXIMATION MULTIVARIABLE FUNCTIONS BY THE RATIONAL EXPRESSION WITH THE INTERPOLATION\",\"authors\":\"P. Malachivskyy, L. Melnychok, Y. Pizyur\",\"doi\":\"10.17721/2706-9699.2022.2.09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p \\\\to \\\\infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.\",\"PeriodicalId\":40347,\"journal\":{\"name\":\"Journal of Numerical and Applied Mathematics\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17721/2706-9699.2022.2.09\",\"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 Numerical and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17721/2706-9699.2022.2.09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
CHEBYSHEV APPROXIMATION MULTIVARIABLE FUNCTIONS BY THE RATIONAL EXPRESSION WITH THE INTERPOLATION
A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p \to \infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.
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