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Least-squares with minimal oversampling

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DREW01 - Multivariate approximation, discretization, and sampling recovery

In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be achieved, in an expected L2 sense, as soon as the sample size m is larger than the dimension n of the approximation space by a constant ratio. On the other hand, for m = n, we obtain an interpolation strategy with a stability factor of order n. This is joint work with Abdellah Chkifa.

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