Wavelet adaptive algorithm for discrete pseudo-differential operators

In this study, we examine biorthogonal wavelets that are tailored to a specific discrete pseudo-differential equation ‎‎‎of the form T_{\sigma}u = f, where T_{\sigma} is an invertible discrete pseudo-differential operator defined on ‎‎‎the lattice \mathbb{Z}^{n} for every f\in\ell^{۲}(\mathbb{Z}^{n})‎‎. Our focus is on computing Galerkin approximations ‎‎‎of the solution to this problem using an adaptive algorithm.‎

Keywords:

Wavelet , Discrete Pseudo-differential operators , Error bound , Galerkin method , Approximation algorithm