Superoptimal approximation for unbounded symbols

The superoptimal Frobenius approximation of Toeplitz matrices is considered in connection with the case of unbounded symbols. In particular, we use the superoptimal approximation as preconditioner for the CG method when a Fisher–Hartwig singularity is present in the symbol, with special regard to systems coming from times series and financial applications. A theoretical discussion concerning classical circulant preconditioners and a numerical comparison with the Strang and with the optimal approximations are presented particularly with reference to the presence of noise.