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We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be recovered from m≍slog4(N) random samples that are chosen independently according to the Chebyshev probability measure dν(x)=π−1(1−x2)−1/2dx. As an efficient recovery...
We consider the recovery of polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random sampling points. We show that a Legendre s-sparse polynomial of maximal degree N can be recovered from m ? s log4(N) random samples that are chosen independently according to the Chebyshev probability measure ??R??1(1 - x2)-1/2dx on [-1; 1]. As an efficient recovery...
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