{"title":"多元多项式稀疏插值的鲁棒算法","authors":"Dai Numahata, Hiroshi Sekigawa","doi":"10.1145/3338637.3338648","DOIUrl":null,"url":null,"abstract":"We consider the problem of symbolic-numeric sparse interpolation of multivariate polynomials. The problem is to find the coefficients and the exponents of a given black-box polynomial [EQUATION] by evaluating the value of <i>f</i>(<i>x</i><sub>1</sub>,..., <i>x<sub>n</sub></i>) at any point in C<sup><i>n</i></sup> in floating-point arithmetic and by using the conditions of the input.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"169 1","pages":"145-147"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Robust algorithms for sparse interpolation of multivariate polynomials\",\"authors\":\"Dai Numahata, Hiroshi Sekigawa\",\"doi\":\"10.1145/3338637.3338648\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of symbolic-numeric sparse interpolation of multivariate polynomials. The problem is to find the coefficients and the exponents of a given black-box polynomial [EQUATION] by evaluating the value of <i>f</i>(<i>x</i><sub>1</sub>,..., <i>x<sub>n</sub></i>) at any point in C<sup><i>n</i></sup> in floating-point arithmetic and by using the conditions of the input.\",\"PeriodicalId\":7093,\"journal\":{\"name\":\"ACM Commun. Comput. Algebra\",\"volume\":\"169 1\",\"pages\":\"145-147\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Commun. Comput. Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3338637.3338648\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Commun. Comput. Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3338637.3338648","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Robust algorithms for sparse interpolation of multivariate polynomials
We consider the problem of symbolic-numeric sparse interpolation of multivariate polynomials. The problem is to find the coefficients and the exponents of a given black-box polynomial [EQUATION] by evaluating the value of f(x1,..., xn) at any point in Cn in floating-point arithmetic and by using the conditions of the input.
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