For a tridiagonal matrix of the from

\begin{bmatrix} a & -b & \newline -b & a & -b \newline & \ddots & \ddots & \ddots \newline & & & & -b \newline & & &-b & a \end{bmatrix}

with $a \geq 2b > 0$ I would like to compare, in funtion of $a$ and $b$, the convergence of the Gauss-Seidel method and the Steepest Descent method. But how to do such a comparison if the information about Gauss-Seidel convergence is given by is spectral radius and the information about the Steepest Descent convergence is given by the ratio between the largest and the smallest eigenvalues?