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

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