Geodesic
Twofold deflation preconditioning of linear algebraic systems. I. Theory
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 95-152 
L. Yu. Kolotilina. Twofold deflation preconditioning of linear algebraic systems. I. Theory. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 95-152. http://geodesic.mathdoc.fr/item/ZNSL_1995_229_a3/
@article{ZNSL_1995_229_a3,
     author = {L. Yu. Kolotilina},
     title = {Twofold deflation preconditioning of linear algebraic {systems.~I.~Theory}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--152},
     year = {1995},
     volume = {229},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_229_a3/}
}
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In this paper, preconditioning of linear algebraic systems with symmetric positive-definite coefficient matrices by deflation is considered. The twofold deflation technique for simultaneously deflating largest $s$ and smallest $s$ eigenvalues using an appropriate deflating subspace of dimension $s$ is suggested. The possibility of using the extreme Ritz vectors of the coefficient matrix for deflation is analyzed. Bibliography: 15 titles.