analytical inversion of general periodic tridiagonal matrices

In this paper we present an analytical forms for the inversion of general periodic tridiagonal 
matrices, and provide some very simple analytical forms which immediately lead to closed 
formulae for some special cases such as symmetric or perturbed Toeplitz for both periodic 
and non-periodic tridiagonal matrices. An efficient computational algorithm for finding the 
inverse of any general periodic tridiagonal matrices from the analytical form is given, it is 
suited for implementation using Computer Algebra systems such as MAPLE, MATLAB, ...