Kahan's KGD step-size is shown to converge at least R-linearly with rate 1-1/cond(H) for quadratics, and an adaptive generalization for general optimization is proved and tested.
Fletcher, Optimization and control with applications, Springer, Boston, MA, 2005, chapter On the Barzilai-Borwein method, 235--256
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Kahan's Automatic Step-Size Control for Unconstrained Optimization
Kahan's KGD step-size is shown to converge at least R-linearly with rate 1-1/cond(H) for quadratics, and an adaptive generalization for general optimization is proved and tested.