Tridiagonal Matrices: lnvertibility and Conditioning*

Tridiagonal matrices arise in a large variety of applications. Most of the time they are diagonally dominant, and this is indeed the case most extensively studied. In this paper we study, in a unified approach, the invertibility and the conditioning of such matrices. The results presented provide practical criteria for a tridiagonal and irreducible matrix to be both invertible and “well conditioned. ” An application to a singular perturbation boundary value problem is then presented. 1