Geodesic
Minimization properties and short recurrences for Krylov subspace methods
Electronic transactions on numerical analysis, Tome 2 (1994), pp. 57-75
It is well known that generalized conjugate gradient (cg) methods, fulfilling a minimization property in the whole spanned Krylov space, cannot be formulated with short recurrences for nonsymmetric system matrices. Here, Krylov subspace methods are proposed that do fulfill a minimization property and can be implemented as short recurrence method at the same time.
Classification : 65F10, 65F50, 40A05
Keywords: conjugate gradients, convergence, linear systems, Krylov methods 
@article{ETNA_1994__2__a9,
     author = {Weiss,  Rudiger},
     title = {Minimization properties and short recurrences for {Krylov} subspace methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {57--75},
     year = {1994},
     volume = {2},
     zbl = {0809.65027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1994__2__a9/}
}
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JO  - Electronic transactions on numerical analysis
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EP  - 75
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/ETNA_1994__2__a9/
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%0 Journal Article
%A Weiss,  Rudiger
%T Minimization properties and short recurrences for Krylov subspace methods
%J Electronic transactions on numerical analysis
%D 1994
%P 57-75
%V 2
%U http://geodesic.mathdoc.fr/item/ETNA_1994__2__a9/
%G en
%F ETNA_1994__2__a9
Weiss,  Rudiger. Minimization properties and short recurrences for Krylov subspace methods. Electronic transactions on numerical analysis, Tome 2 (1994), pp. 57-75. http://geodesic.mathdoc.fr/item/ETNA_1994__2__a9/