An algorithm for symbolic-numeric sparse interpolation of multivariate polynomials whose degree bounds are unknown

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,...x_n) = Σ^t_j=1 c_jx₁^{d_{j, 1}} ...x_n^{d_{j, n}} ∈ C[x₁,...,x_n] (c_j ≠ 0)and the number of terms t, and that we can evaluate the value of f (x¹,...,x_n) at any point in Cⁿ in floating-point arithmetic. The problem is to find the coefficients c₁, ..., c_t and the exponents d_1,1,..., d_t,n. We propose an efficient algorithm to solve the problem.