  The Barzilai-Borwein (BB) steplengths play great roles in practical gradient
methods for solving unconstrained optimization problems. Motivated by the
observation that the two well-known BB steplengths correspond to the ordinary
and the data least squares, respectively, we present a family of BB steplengths
from the viewpoint of scaled total least squares. Numerical experiments
demonstrate that a high performance can be received by a carefully-selected BB
steplength in the new family.
