Banded matrices with banded inverses

Our concern is with the reconstruction of functions from linear observations which only depend locally on the data. We are especially interested in the case that the data and model for reconstruction are "stationary". This leads us to study the solution of rectangular Toeplitz equations which have fewer rows than columns. We can therefore take advantage of excess of unknowns over equations to obtain banded inverses, even when the original system is banded. © 1992.