Geodesic
Quasi-Newton preconditioners for the inexact Newton method
Electronic transactions on numerical analysis, Tome 23 (2006), pp. 76-87
In this paper preconditioners for solving the linear systems of the Newton method in each nonlinear iteration are studied. In particular, we define a sequence of preconditioners built by means of Broyden-type rank-one updates. Optimality conditions are derived which guarantee that the preconditioned matrices are not far from the identity in a matrix norm. Some notes on the implementation of the corresponding inexact Newton method are given and some numerical results on two model problems illustrate the application of the proposed preconditioners.
Classification : 65F10, 65H10, 15A12
Keywords: quasi-Newton method, Krylov iterations, updating preconditioners, inexact Newton method 
@article{ETNA_2006__23__a14,
     author = {Bergamaschi,  L. and Bru,  R. and Mart{\'\i}nez,  A. and Putti,  M.},
     title = {Quasi-Newton preconditioners for the inexact {Newton} method},
     journal = {Electronic transactions on numerical analysis},
     pages = {76--87},
     year = {2006},
     volume = {23},
     zbl = {1112.65045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__23__a14/}
}
TY  - JOUR
AU  - Bergamaschi,  L.
AU  - Bru,  R.
AU  - Martínez,  A.
AU  - Putti,  M.
TI  - Quasi-Newton preconditioners for the inexact Newton method
JO  - Electronic transactions on numerical analysis
PY  - 2006
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EP  - 87
VL  - 23
UR  - http://geodesic.mathdoc.fr/item/ETNA_2006__23__a14/
LA  - en
ID  - ETNA_2006__23__a14
ER  - 
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%A Bru,  R.
%A Martínez,  A.
%A Putti,  M.
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%J Electronic transactions on numerical analysis
%D 2006
%P 76-87
%V 23
%U http://geodesic.mathdoc.fr/item/ETNA_2006__23__a14/
%G en
%F ETNA_2006__23__a14
Bergamaschi,  L.; Bru,  R.; Martínez,  A.; Putti,  M. Quasi-Newton preconditioners for the inexact Newton method. Electronic transactions on numerical analysis, Tome 23 (2006), pp. 76-87. http://geodesic.mathdoc.fr/item/ETNA_2006__23__a14/