Solving Bezout-like polynomial equations for the design of interpolatory subdivision schemes

In this paper the problem of designing interpolatory subdivision schemes is considered. The idea is to modify a given approximating subdivision scheme just enough to satisfy the interpolation requirement. This leads to the solution of a generalized Bezout polynomial equation possibly involving more than two polynomials. By exploiting the matrix counterpart of this equation it is shown that small-degree solutions can be generally found by inverting an associated structured matrix of Toeplitz-like form. If the approximating scheme is defined in terms of a free parameter, then the inversion can be performed by numeric-symbolic methods.