Geodesic
On the spectral properties of an operator pencil
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 197-205

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For a broad class of iterative algorithms for solving saddle point problems, the study of the convergence and of the optimal properties can be reduced to an analysis of the eigenvalues of operator pencils of a special form. A new approach to analyzing spectral properties of pencils of this kind is proposed that makes it possible to obtain sharp estimates for the convergence rate. 
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     author = {Yu. V. Bychenkov},
     title = {On the spectral properties of an operator pencil},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a3/}
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Yu. V. Bychenkov. On the spectral properties of an operator pencil. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 197-205. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a3/