<ul><li>Researchers have proven sharp upper and lower bounds for the approximation of Sobolev functions by sums of multivariate ridge functions.</li><li>The order of approximation asymptotically behaves as n^(-r/(d-l)), where r is the regularity of the Sobolev functions to be approximated.</li><li>The lower bound even holds when approximating L^∞-Sobolev functions of regularity r with error measured in L^1.</li><li>The upper bound applies to the approximation of L^p-Sobolev functions in L^p for any 1 ≤ p ≤ ∞.</li></ul>

On best approximation by multivariate ridge functions with applications to generalized translation networks

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