Interpolation of Shifted-Lacunary Polynomials
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The computed sparsity t is absolutely minimal over any shifted power basis. The novelty of our algorithm is that the complexity is polynomial in the (sparse) representation size, which may be logarithmic in the degree of f. Our method combines previous celebrated results on sparse interpolation and computing sparsest shifts, and provides a way to handle polynomials with extremely high degree which are, in some sense, sparse in information.
Keywords.Sparse interpolation sparsest shift lacunary polynomials
Subject classification.Primary 68W30 Secondary 12Y05
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