Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs (Q2036421)

The main concern of the authors is the numerical approximation of solutions to boundary value problems attached to PDEs, based on compressive sensing via the CORSING (COmpRessed SolvING) method. Actually they work on weak problems formulated in Hilbert spaces. The main idea of the compressed solving is to lighten the computational cost characterizing a Petrov-Galerkin discretization method, the so called curse of dimensionality, by reducing the dimension of the test space with respect to the trial space. In the present paper the authors provide a new analysis of the restricted isometry constants and null space property of matrices arising from random sampling in bounded Riesz systems. With this result they considerably improve the theoretical guarantees for the CORSING method.