{"title":"非周期函数混合导数的最优恢复方法","authors":"Y. V. Semenova, S. G. Solodky","doi":"10.17721/2706-9699.2022.2.16","DOIUrl":null,"url":null,"abstract":"The problem of numerical differentiation for non-periodic bivariate functions is investigated. For the recovering mixed derivatives of such functions an approach on the base of truncation method is proposed. The constructed algorithms deal with Legendere polynomials, the degree of which is chosen so as to minimize the approximation error. It is established that these algorithms are order-optimal both in terms of accuracy and in the sense of the amount of Galerkin information involved.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"118 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"OPTIMAL METHODS FOR RECOVERING MIXED DERIVATIVES OF NON-PERIODIC FUNCTIONS\",\"authors\":\"Y. V. Semenova, S. G. Solodky\",\"doi\":\"10.17721/2706-9699.2022.2.16\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of numerical differentiation for non-periodic bivariate functions is investigated. For the recovering mixed derivatives of such functions an approach on the base of truncation method is proposed. The constructed algorithms deal with Legendere polynomials, the degree of which is chosen so as to minimize the approximation error. It is established that these algorithms are order-optimal both in terms of accuracy and in the sense of the amount of Galerkin information involved.\",\"PeriodicalId\":40347,\"journal\":{\"name\":\"Journal of Numerical and Applied Mathematics\",\"volume\":\"118 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/10.17721/2706-9699.2022.2.16\",\"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/10.17721/2706-9699.2022.2.16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
OPTIMAL METHODS FOR RECOVERING MIXED DERIVATIVES OF NON-PERIODIC FUNCTIONS
The problem of numerical differentiation for non-periodic bivariate functions is investigated. For the recovering mixed derivatives of such functions an approach on the base of truncation method is proposed. The constructed algorithms deal with Legendere polynomials, the degree of which is chosen so as to minimize the approximation error. It is established that these algorithms are order-optimal both in terms of accuracy and in the sense of the amount of Galerkin information involved.
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