Error Localization of Best $L_{1}$ Polynomial Approximants

An important observation in compressed sensing is that the $\ell_0$ minimizer of an underdetermined linear system equal to $\ell_1$ when there exists a sparse solution vector and certain restricted isometry property holds. Here, we develop continuous analogue this show best $L_0$ $L_1$ polynomial approximants corrupted on set small measure are nearly equal. We demonstrate error localization use our observations improved algorithm for computing functions.