Sparse Rational Function Interpolation with Finitely Many Values for the Coefficients

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10693)


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 unique integer k. Experimental results show that the univariate interpolation algorithm is almost optimal.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.KLMM, UCAS, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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