157 1994 Lina Hemmingsson and Kurt Otto lina@tdb.uu.se Analysis of Semi-Toeplitz Preconditioners for First-order PDEs Abstract A semi-Toeplitz preconditioner for nonsymmetric, nondiagonally dominant systems of equations is studied. The preconditioner solve is based on a Fast Modified Sine Transform. As a model problem we study a system of equations arising from an implicit time-discretization of a scalar hyperbolic PDE. Analytical formulas for the eigenvalues and the eigenvectors of the preconditioned system are derived. The convergence of a minimal residual iteration is shown to depend only on the grid ratio in space and not on the number of unknowns.