{"title":"在实数和复数域上计算多项式的计算复杂度","authors":"V. Pan","doi":"10.1145/800133.804344","DOIUrl":null,"url":null,"abstract":"Fast computation of polynomials of 1 variable in the fields R and C of real and complex numbers is considered. The optimal schemes of computation with preconditioning (that is, the schemes involving the minimal number of arithmetic operations without counting preliminary treatment of coefficients) for evaluation in C are presented. The schemes which are close to optimal ones are presented for evaluation in R. The difference between the complexity of computation in R and in C is established. A new generalization of the problem is presented.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Computational complexity of computing polynomials over the fields of real and complex numbers\",\"authors\":\"V. Pan\",\"doi\":\"10.1145/800133.804344\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Fast computation of polynomials of 1 variable in the fields R and C of real and complex numbers is considered. The optimal schemes of computation with preconditioning (that is, the schemes involving the minimal number of arithmetic operations without counting preliminary treatment of coefficients) for evaluation in C are presented. The schemes which are close to optimal ones are presented for evaluation in R. The difference between the complexity of computation in R and in C is established. A new generalization of the problem is presented.\",\"PeriodicalId\":313820,\"journal\":{\"name\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800133.804344\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the tenth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800133.804344","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computational complexity of computing polynomials over the fields of real and complex numbers
Fast computation of polynomials of 1 variable in the fields R and C of real and complex numbers is considered. The optimal schemes of computation with preconditioning (that is, the schemes involving the minimal number of arithmetic operations without counting preliminary treatment of coefficients) for evaluation in C are presented. The schemes which are close to optimal ones are presented for evaluation in R. The difference between the complexity of computation in R and in C is established. A new generalization of the problem is presented.