A. Dur and J. Grabmeier. Applying coding theory to sparse interpolation. SIAM Journal on Computing, 22(4):695--704, August 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for interpolating sparse multivariate polynomials over such fields. Grigoriev, Karpinski and Singers [13] and Clausen et al. 8] consider the problem of interpolating a sparse polynomial over various finite fields (see also the related work of Dress and Grabmeier [9] and Dur and Grabmeier [10]) However, for small fields (such as GF(p) where p is a small prime) their algorithms are efficient only if queries can be made over a larger extension field. For the field GF(2) when no such extension is made, Clausen et al. show that t sparse, n variable polynomials can be efficiently ....

A. Dur and J. Grabmeier. Applying coding theory to sparse interpolation. SIAM Journal on Computing, 22(4):695--704, August 1993.

....are GF 2, small finite fields, or large finite (and infinite) fields. For GF 2, a related problem has been studied, in which the maximum number of coefficients, t, is known in advance (so called t sparse interpolation) An effective procedure exists for selecting the interpolation points [11] [3] and solving the problem using the theory of error correcting codes. For the case of large finite and infinite fields, an algorithm for t sparse interpolation exists [1] that relies heavily on the largeness of the field. The practicality of this algorithm is diminished by the computations with ....

A. Dur and J. Grabmeier. Applying coding theory to sparse interpolation. SIAM Journal of Computing, 22(4):695--703, August 1993.

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