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- W2773691209 abstract "In this paper, a new Monte Carlo interpolation algorithm for sparse multivariate polynomials is given based on the idea of randomized Kronecker substitution. The main contribution is a new method to reduce multivariate polynomial interpolation to that of univariate polynomials, which leads to better computational complexities. For an $n$-variate black-box polynomial $f$ with a degree bound $D$ and a term bound $T$, if the coefficients of $f$ are taken from an integral domain $R$, the algorithm needs $O^thicksim(nTD)$ evaluations plus $O^thicksim(nTD)$ $R$ operations. If the coefficients of $f$ are taken from a finite field $F_q$, the algorithm needs $O^thicksim(nT)$ evaluations plus $O^thicksim(nTDlog q)$ bit operations. This is the first reduction based algorithm whose complexity is linear in $n,T,D,log q$." @default.
- W2773691209 created "2017-12-22" @default.
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- W2773691209 creator A5043767154 @default.
- W2773691209 date "2017-12-15" @default.
- W2773691209 modified "2023-09-27" @default.
- W2773691209 title "Revisit Randomized Kronecker Substitution based Sparse Polynomial Interpolation." @default.
- W2773691209 hasPublicationYear "2017" @default.
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