Geodesic
New implicit multi-step quasi-Newton methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 2, pp. 189-200.

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Multi-step quasi-Newton methods for optimization use data from more than one previous step to construct the current Hessian approximation. These methods were introduced by Ford and Moughrabi in [3,4], where they showed how to construct such methods by means of interpolating curves. To produce a better parametrization of the interpolation, Ford [2] developed the idea of “implicit” methods. In this paper, we describe the derivation of new implicit updates which are similar to the methods $\mathbf{14}$ and $\mathbf{15}$ developed in [7]. The experimental results we present here show that both of the new methods produce better performance than the existing methods, particularly as the dimension of the test problem grows. 
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I. A. R. Mograbi. New implicit multi-step quasi-Newton methods. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 2, pp. 189-200. http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a5/

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