TOEPLITZ PRECONDITIONERS WITH BLOCK STRUCTURE FOR FIRST-ORDER PDES

Preconditioners to nonsymmetric, nondiagonally dominant systems of equ ations are constructed and examined numerically. The preconditioners a re based on a Toeplitz approach with a certain symmetry that we define . The inversion of the preconditioners is defined through a Fast Modif ied Sine Transform. As a model problem we study the systems of equatio ns arising from an implicit time-discretization with a large time-step of a scalar hyperbolic PDE.