In the last 15 years there has been an intensive work on iterative solvers (essentially PCG and multigrid) for Toeplitz linear systems. In some contexts we have a satisfactory picture of results, algorithms and theoretical analysis; in other contexts some questions have been answered in the negative and finally there are important problems that are still open. In this talk we focus our attention mainly on open, challenging problems, trends and future work.
1 Joint work with Cristina TABLINO POSSIO.