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arXiv · 1706.00914

Sparse Rational Function Interpolation with Finitely Many Values for the Coefficients

Qiao-Long Huang·Xiao-Shan Gao
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Abstract

In this paper, we give new sparse interpolation algorithms for black box univariate and multivariate rational functions h=f/g whose coefficients are integers with an upper bound. The main idea is as follows: choose a proper integer beta and let h(beta) = a/b with gcd(a,b)=1. Then f and g can be computed by solving the polynomial interpolation problems f(beta)=ka and g(beta)=ka for some integer k. It is shown that the univariate interpolation algorithm is almost optimal and multivariate interpolation algorithm has low complexity in T but the data size is exponential in n.

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Qiao-Long Huang, Xiao-Shan Gao. 2017-06-03. Sparse Rational Function Interpolation with Finitely Many Values for the Coefficients. https://arxiv.org/abs/1706.00914

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