Geodesic
Generalized method of conjugate gradients for the solution of linear systems
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 181-188 
G. V. Savinov. Generalized method of conjugate gradients for the solution of linear systems. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 181-188. http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a9/
@article{ZNSL_1978_80_a9,
     author = {G. V. Savinov},
     title = {Generalized method of conjugate gradients for the solution of linear systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {181--188},
     year = {1978},
     volume = {80},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a9/}
}
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TI  - Generalized method of conjugate gradients for the solution of linear systems
JO  - Zapiski Nauchnykh Seminarov POMI
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VL  - 80
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a9/
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ID  - ZNSL_1978_80_a9
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We obtain convergence criteria for the generalized method of conjugate gradients for solving systems of linear algebraic equations; they imply the convergence of the method in a finite number of steps. The theorem proved in the paper allows at the same time to consider the known variants of the generalized method of conjugate gradients, as well as to devise new modifications for the convergence of this method.