Numerical linear algebra is a recurrent theme in our research. Usually, the focus is on iteration methods for linear systems of equations, e.g., the method of conjugate gradients or semiiterative methods. In our analysis, we often exploit the appealing connection of these methods to orthogonal polynomials and approximation theory.
This is quite similar for matrices with Toeplitz or related structures, as they appear in signal or image processing, for example. Tools from harmonic analysis can be used to construct preconditioners wich allow a very efficient solution of linear systems with these matrices.