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 Tσu = f, where Tσ is an invertible discrete pseudo-differential operator defined on the lattice Z n for every f ∈ ℓ ² (Z n ). Our focus is on computing Galerkin approximations of the solution to this problem using an adaptive algorithm.