Geodesic
O n the theory of the generalized augmented matrix preconditioning method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 4, pp. 335-343.

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This paper is devoted to an improvement of the theory of the recently proposed generalized augmented matrix preconditioning method [5]. Namely, we compute a sharp lower bound on the eigenvalues of a preconditioned matrix based on the properties of a projector involved in its definition. 
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M. R. Larin; A. Padiy. O n the theory of the generalized augmented matrix preconditioning method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 4, pp. 335-343. http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a5/

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[6] Padiy A., Larin M., Model analysis of a subspace correction technique for anisotropic diffusion problems, Internal report No 9818, University of Nijmegen, 1998