Dai Numahata
Abstract
We consider the problem of sparse interpolation of a multivariate black-box polynomial in floatingpoint arithmetic. More specifically, we assume that we are given a black-box polynomial f (x1,...xn) = Σtj=1 cjx1dj, 1 ...xndj, n ∈ C[x1,...,xn] (cj ≠ 0)and the number of terms t, and that we can evaluate the value of f (x1,...,xn) at any point in Cn in floating-point arithmetic. The problem is to find the coefficients c1, ..., ct and the exponents d1,1,..., dt,n. We propose an efficient algorithm to solve the problem.
- M. Ben-Or and P. Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. In Proc. Twentieth Annual ACM Symp. Theory Comput., pages 301--309, New York, N.Y., 1988. ACM Press. Google Scholar
Digital Library
- A. Cuyt ad W.-s. Lee. A new algorithm for sparse interpolation of multivariate polynomials. Theoretical Comput. Sci., 409(2):180--185, 2008. Google ScholarDigital Library
- M. Giesbrecht, G. Labahn, and W.-s. Lee. Symbolic-numeric sparse interpolation of multivariate polynomials. J. Symb. Comput., 44:943--959, 2009. Google ScholarDigital Library
Index Terms
- An algorithm for symbolic-numeric sparse interpolation of multivariate polynomials whose degree bounds are unknown
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