Random sampling and approximation of signals with bounded derivatives

Multivariate approximation of functions with bounded fractional derivatives

In this paper we use a piecewise constant Smolyak approximation algorithm to approximate functions whose partial mixed fractional derivatives of order 0 < α ≤ 1 in each variable are bounded. We prove that the L1 error of our approximation is of order (log card(Aq,s))(card(Aq,s)), where card(Aq,s) denotes the number of function evaluations used by the algorithm.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L and tensorized H 0 simultaneously on a standard k-dimensional cube. In the special case k = 2 the suggested ...

Random sampling of bandlimited signals on graphs

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, n...

Fast Eigenspace Approximation using Random Signals

We focus in this work on the estimation of the first k eigenvectors of any graph Laplacian using filtering of Gaussian random signals. We prove that we only need k such signals to be able to exactly recover as many of the smallest eigenvectors, regardless of the number of nodes in the graph. In addition, we address key issues in implementing the theoretical concepts in practice using accurate a...

Interpolants with Bounded Derivatives