Biorthogonal Wavelets and Multigrid

We will be concerned with the solution of an elliptic boundary, value problem in one dimension with polynomial coefficients. In a Galerkin approach, we employ biorthogonal wavelets adapted to a differential operator with constant coefficients, and use the refinement equations to set up the system of linear equations with exact entries (up to round-off). For the solution of the linear equation, we construct a biorthogonal two-grid method with intergrid operators stemming from wavelet-type operators adapted to the problem.