In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately $4 m n$ multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm~1, proposed in this report, confirm its practical efficiency.
Report V-1059, Institute of Computer Science AS CR, Pod Vodarenskou Vezi 2, 18207 Prague 8, 2010.