A Schur algorithm for symmetric inner functions

Symmetric inner rational functions naturally arise in the description of physical systems which satisfy the conservation and reciprocity laws. Inner matrix functions can be parametrized by a sequence of interpolation vectors obtained from a tangential Schur algorithm. In this paper, we present a Schur type algorithm which allows to describe symmetric inner functions, based on a two-sided Nudelman interpolation problem. This Schur algorithm gives rise to an interesting interpretation in the context of surface acoustic wave filters.