Faster sparse multivariate polynomial interpolation of straight-line programs
نویسندگان
چکیده
منابع مشابه
Faster Sparse Multivariate Polynomial Interpolation of Straight-Line Programs
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a multivariate polynomial, with coefficients in an arbitrary finite field, and with a reasonable number of nonzero terms but possibly very large degree. It is co...
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We give a new probabilistic algorithm for interpolating a “sparse” polynomial f given by a straight-line program. Our algorithm constructs an approximation f of f , such that f − f probably has at most half the number of terms of f , then recurses on the difference f−f. Our approach builds on previous work by Garg and Schost (2009), and Giesbrecht and Roche (2011), and is asymptotically more ef...
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We present a faster Monte Carlo algorithm for the interpolation of a straightline program to find a sparse polynomial f over an arbitrary finite field of size q. We assume a priori bounds D and T are given on the degree and number of terms of f . The approach presented in this paper is a hybrid of the diversified and recursive interpolation algorithms, the two previous fastest known probabilist...
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In this paper, we propose new deterministic interpolation algorithms and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let f be an n-variate polynomial with a degree bound D and and term bound T . Our deterministic algorithms have better complexities than existing deterministic interpolation algorithms in most cases. Our Monte Ca...
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We consider the problem of interpolating sparse multivariate polynomials from their values. We discuss two algorithms for sparse interpolation, one due to Ben-Or and Tiwari (1988) and the other due to Zippel (1988). We present efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2016
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2015.11.005