On the Barzilai and Borwein choice of steplength for the gradient method

In a recent paper, Barzilai and Borwein presented a new choiceof steplength for the gradient method. Their choice does notguarantee descent in the objective function and greatly speedsup the convergence of the method. They presented a convergenceanalysis of their method only in the two-dimensional quadraticcase. We establish the convergence of the Barzilai and Borweingradient method when applied to the minimization of a strictlyconvex quadratic function of any number of variables.