On the additive structure of the inverses of banded matrices

The additive structure of the inverses of banded matrices is investigated. Under certain conditions, the inverse of a (2k+1)-diagonal symmetric banded matrix can be expressed as a sum of k symmetric matrices belonging to the class of inverses of symmetric irreducible tridiagonal matrices. In the nonsymmetric case, a more complicated structure is obtained. Applications are mentioned for the resolution of constant coefficient banded linear systems in VLSI models.