Geodesic
Broyden updating, the good and the bad!
Documenta mathematica, Optimization Stories (2012), pp. 301-315.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

So far so good! We had an updating procedure (the `ful secant method') that seemed to work provided that certain conditions of linear independence were satisfied, but the problem was that it did not work very well. In fact, it proved to be quite numerically unstable. (cf. [C. G. Broyden, On the discovery of the "good Broyden" method, Math. Program. 87, No. 2 (B), 209--213 (2000; Zbl 0970.90002)])
Classification : 65H10
Keywords: quasi-Newton, secant condition, least change, bounded deterioration, superlinear convergence 
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     title = {Broyden updating, the good and the bad!},
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Griewank, Andreas. Broyden updating, the good and the bad!. Documenta mathematica, Optimization Stories (2012), pp. 301-315. http://geodesic.mathdoc.fr/item/DOCMA_2012__S3__a12/