  The Barzilai-Borwein (BB) method has demonstrated great empirical success in
nonlinear optimization. However, the convergence speed of BB method is not well
understood, as the known convergence rate of BB method for quadratic problems
is much worse than the steepest descent (SD) method. Therefore, there is a
large discrepancy between theory and practice. To shrink this gap, we prove
that the BB method converges $R$-linearly at a rate of $1-1/\kappa$, where
$\kappa$ is the condition number, for strongly convex quadratic problems. In
addition, an example with the theoretical rate of convergence is constructed,
indicating the tightness of our bound.
