{"title":"最接近的低次多项式","authors":"Robert M Corless, N. Rezvani","doi":"10.1145/1277500.1277530","DOIUrl":null,"url":null,"abstract":"Suppose one is working with the polynomial p(x) = −0.99B3 0(x)−1.03B 1(x)− 0.33B 2(x) + B 3 3(x) expressed in terms of degree 3 Bernstein polynomials and suppose one has reason to believe that p(x) is really of degree 2. Applying the degree-reducing procedure [6] one gets −0.99B2 0(x)− 1.05B 1(x) + B 2(x). But is this correct, or have we treated p(x) in a Procrustean 1 fashion? Checking by converting p(x) to the power basis, we find that the coefficient of x is 0.11. Is this zero or not?","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"106 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"The nearest polynomial of lower degree\",\"authors\":\"Robert M Corless, N. Rezvani\",\"doi\":\"10.1145/1277500.1277530\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Suppose one is working with the polynomial p(x) = −0.99B3 0(x)−1.03B 1(x)− 0.33B 2(x) + B 3 3(x) expressed in terms of degree 3 Bernstein polynomials and suppose one has reason to believe that p(x) is really of degree 2. Applying the degree-reducing procedure [6] one gets −0.99B2 0(x)− 1.05B 1(x) + B 2(x). But is this correct, or have we treated p(x) in a Procrustean 1 fashion? Checking by converting p(x) to the power basis, we find that the coefficient of x is 0.11. Is this zero or not?\",\"PeriodicalId\":308716,\"journal\":{\"name\":\"Symbolic-Numeric Computation\",\"volume\":\"106 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symbolic-Numeric Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1277500.1277530\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symbolic-Numeric Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1277500.1277530","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Suppose one is working with the polynomial p(x) = −0.99B3 0(x)−1.03B 1(x)− 0.33B 2(x) + B 3 3(x) expressed in terms of degree 3 Bernstein polynomials and suppose one has reason to believe that p(x) is really of degree 2. Applying the degree-reducing procedure [6] one gets −0.99B2 0(x)− 1.05B 1(x) + B 2(x). But is this correct, or have we treated p(x) in a Procrustean 1 fashion? Checking by converting p(x) to the power basis, we find that the coefficient of x is 0.11. Is this zero or not?
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