A note on a three-term recurrence for a tridiagonal matrix

摘要

In this article the author shows that under certain conditions a three-term recurrence for a tridiagonal matrix becomes a two-term recurrence. Using this new recurrence, the possibility of the LU factorization of any tridiagonal matrix is now easy to investigate. The positive definiteness of any real symmetric tridiagonal matrix is now easy to check. An algorithm for solving any linear system with positive definite tridiagonal matrix is given. Some numerical examples are given.