A new Barzilai-Borwein steplength from the viewpoint of total least squares

Barzilai-Borwein (BB) steplength is a popular choice in gradient descent method. By observing that the two existing BB steplengths correspond to the ordinary and the data least squares, respectively, we employ the third kind of least squares, the total least squares, to create a new BB steplength, which is shown to lie between the two existing BB steplengths.