Let q ≥ 1 be an integer, Sq denote the unit sphere embedded in the Euclidean space Rq+1, and µq be its Lebesgue surface measure. We establish upper and lower bounds for sup f...
Compressed sensing is a new area of signal processing. Its goal is to minimize the number of samples that need to be taken from a signal for faithful reconstruction. The performan...
We construct simple algorithms for high-dimensional numerical integration of function classes with moderate smoothness. These classes consist of square-integrable functions over t...
We extend the lower bounds on the complexity of computing Betti numbers proved in [6] to complex algebraic varieties. More precisely, we first prove that the problem of deciding ...
We study the complexity of approximating the smallest eigenvalue of −∆ + q with Dirichlet boundary conditions on the d-dimensional unit cube. Here ∆ is the Laplacian, and th...
A discontinuous Galerkin (DG) discretization of Dirichlet problem for second-order elliptic equations with discontinuous coefficients in 2-D is considered. For this discretization...