# Tridiagonal Matrix

What is the most efficient way to calucate the dominant eigenvector of a real symmetric tridiagonal matrix, and what's the corresponding time complexity bound? Could someone give me a reference for this special structure? Thank you in advance.

-
It's been a while since I looked in Golub & van Loan's book, but have you tried that? –  Yemon Choi Mar 6 '11 at 6:51
Lanczos algorithm (en.wikipedia.org/wiki/Lanczos_algorithm) is generally well-suited to obtain the dominant eigenvector. –  Fabian Mar 6 '11 at 8:43

The following paper proposes an $O(nk)$ algorithm called $MR^3$ (Multiple Relatively Robust Representations) to compute $k$ orthogonal eigenvectors of an $n \times n$ symmetric tridiagonal matrix. An implementation of this method is also available in LAPACK.