Convergent filtered scheme for the Monge-Amp\`ere Equation

We propose an extension to our monotone and convergent method for the Monge-Amp`{e}re equation in dimension $d\ge 2$, that incorporates the idea of filtered schemes. The method combines our original monotone operator with a more accurate non-monotone modification, using an appropriately chosen filter. This results in a remarkable improvement of accuracy, but without sacrificing the convergence to the unique viscosity solution.