Sparse Rational Function Interpolation with Finitely Many Values for the Coefficients
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چکیده
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 β and let h(β) = a/b with gcd(a, b) = 1. Then f and g can be computed by solving the polynomial interpolation problems f(β) = ka and g(β) = 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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تاریخ انتشار 2017