{"title":"Sparse Polynomial Interpolation","authors":"Oris Van Der, Oeven","doi":"10.1142/9781786348548_0006","DOIUrl":"https://doi.org/10.1142/9781786348548_0006","url":null,"abstract":"Consider a multivariate polynomial f ∈K[x1, . . . , xn] over a field K, which is given through a black box capable of evaluating f at points in Kn, or possibly at points in An for any K-algebra A. The problem of sparse interpolation is to express f in its usual form with respect to the monomial basis. We analyze the complexity of various old and new algorithms for this task in terms of bounds D and T for the total degree of f and its number of terms. We mainly focus on the case when K is a finite field and explore possible speed-ups under suitable heuristic assumptions.","PeriodicalId":235856,"journal":{"name":"The Moment-SOS Hierarchy","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121424168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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