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- W2776806487 abstract "We consider the sparse polynomial approximation of a multivariate function on a tensor product domain from samples of both the function and its gradient. When only function samples are prescribed, weighted $ell^1$ minimization has recently been shown to be an effective procedure for computing such approximations. We extend this work to the gradient-augmented case. Our main results show that for the same asymptotic sample complexity, gradient-augmented measurements achieve an approximation error bound in a stronger Sobolev norm, as opposed to the $L^2$-norm in the unaugmented case. For Chebyshev and Legendre polynomial approximations, this sample complexity estimate is algebraic in the sparsity $s$ and at most logarithmic in the dimension $d$, thus mitigating the curse of dimensionality to a substantial extent. We also present several experiments numerically illustrating the benefits of gradient information over an equivalent number of function samples only." @default.
- W2776806487 created "2018-01-05" @default.
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- W2776806487 date "2017-12-18" @default.
- W2776806487 modified "2023-10-14" @default.
- W2776806487 title "Compressive Hermite interpolation: sparse, high-dimensional approximation from gradient-augmented measurements" @default.
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- W2776806487 doi "https://doi.org/10.48550/arxiv.1712.06645" @default.
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