Tridiagonal matrices: Invertibility and conditioning (Q1185055)

The authors consider conditioning of a tridiagonal matrix \(T\), normalized to have unit diagonal, \(\tau_ 1, \dots, \tau_{n-1}\) on the superdiagonal and \(\sigma_ 1, \dots, \sigma_{n-1}\) on the subdiagonal. The cases \(\sigma_ i \tau_ i > 0\) for all \(i\), and \(\sigma_ i \tau_ i < 0\) for all \(i\), are analyzed in detail. An exact formula for the condition number of a general \(T\) was given by \textit{N. J. Higham} [SIAM J. Sci. Statist. Comput. 7, No. 1, 150-165 (1986; Zbl 0599.65026)].