Raydan, Marcos2018-06-182018-06-181990-05Raydan, Marcos. "On the Barzilai and Borwein Choice of Steplength for the Gradient Method." (1990) <a href="https://hdl.handle.net/1911/101676">https://hdl.handle.net/1911/101676</a>.https://hdl.handle.net/1911/101676In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. We derive an interesting relationship between the Barzilai and Borwein gradient method and the shifted power method. This relationship allows us to establish the convergence of the Barzilai and Borwein method when applied to the problem of minimizing a strictly convex quadratic function (Barzilai and Borwein considered only 2-dimensional problems). Our point of view also allows us to explain the remarkable improvement obtained by using this new choice of steplength. Finally, for the 2-dimensional case we present some very interesting convergence rate results. We show that our Q and R-rate of convergence analysis is sharp and we compare it with the Barzilai and Borwein analysis.17 ppengTechnical reportTR90-11