Here are some Matlab routines for solving unbalanced band Toeplitz systems.
These routines implements three methods described in P. Favati, G. Lotti, O. Menchi "Recursive algorithms for unbalanced banded Toeplitz systems", namely cr, mcr and st methods. Problem_data is an example of routine for constructing the input data. It provides a random matrix with diagonal dominance, by constructing the first row and column. Moreover, in a simulation context, problem_data constructs the right hand-side from a given solution sol.