Sparse Interpolation of Symmetric Polynomials
نویسندگان
چکیده
منابع مشابه
Randomized Interpolation and Approximation of Sparse Polynomials
We present a randomized algorithm that interpolates a sparse polynomial in polynomial time in the bit complexity model. The algorithm can be also applied to approximate polynomials that can be approximated by sparse polynomials (the approximation is in the L 2 norm).
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We give a quasi-polynomial time algorithm for the problem of interpolating sparse polynomials over integer residue class ringsZm from their values given by a black box. This is a further development of [10].
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To reconstruct a black box multivariate sparse polynomial from its floating point evaluations, the existing algorithms need to know upper bounds for both the number of terms in the polynomial and the partial degree in each of the variables. Here we present a new technique, based on Rutishauser’s qd-algorithm, inwhichwe overcome both drawbacks. © 2008 Elsevier B.V. All rights reserved.
متن کاملInterpolation and Approximation of Sparse Multivariate Polynomials over GF(2)
A function f : {0, 1} → {0, 1} is called t-sparse if the n-variable polynomial representation of f over GF (2) contains at most t monomials. Such functions are uniquely determined by their values at the so-called critical set of all binary n-tuples of Hamming weight ≥ n− ⌊log2 t⌋ − 1. An algorithm is presented for interpolating any t-sparse function f , given the values of f at the critical set...
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Can a quantum computer efficiently interpolate polynomials? We consider blackbox algorithms that seek to learn information about a polynomial f from input/output pairs (xi, f(xi)). We define a more general class of (d, S)-independent function properties, where, outside of a set S of exceptions, knowing d input values does not help one predict the answer. There are essentially two strategies to ...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1997
ISSN: 0196-8858
DOI: 10.1006/aama.1996.0508