Complexity of Weighted Approximation over Rd

Complexity of Weighted Approximation over Rd

We study approximation of univariate functions deened over the reals. We assume that the rth derivative of a function is bounded in a weighted L p norm with a weight. Approximation algorithms use the values of a function and its derivatives up to order r ? 1. The worst case error of an algorithm is deened in a weighted L q norm with a weight. We study the worst case (information) complexity of ...

Worst Case Complexity of Weighted Approximation and Integration over Rd

We study the worst case complexity of weighted approximation and integration for functions deened over R d. We assume that the functions have all partial derivatives of order up to r uniformly bounded in a weighted L p-norm for a given weight function. The integration and the error for approximation are deened in a weighted sense for another given weight %. We present a necessary and suucient c...

Complexity of Weighted Approximation over

We study approximation of univariate functions deened over the reals. We assume that the rth derivative of a function is bounded in a weighted L p norm with a weight. Approximation algorithms use the values of a function and its derivatives up to order r ? 1. The worst case error of an algorithm is deened in a weighted L q norm with a weight. We study the worst case (information) complexity of ...

Average Case Complexity of Weighted Approximation and Integration over R+

The sample complexity of weighted sparse approximation

For Gaussian sampling matrices, we provide bounds on the minimal number of measurements m required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the true underlying support. Our main contribution is that for a sparse vector x ∈ R supported on an unknown set S ⊂ {1, 2, . . . , N} with |S| ≤ k, if S has weighted...