Pub Date : 1900-01-01DOI: 10.1142/9781786348548_0006
Oris Van Der, Oeven
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.
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