Geodesic
Bi-Newton's method for computing spectral projectors
Numerical methods and programming, Tome 15 (2014) no. 1, pp. 121-129.

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An efficient Newton-like method for computing the spectral projector associated with a separated group of eigenvalues near a specified shift of a large sparse matrix is proposed and justified. A number of numerical experiments with a discrete analogue of the non-Hermitian elliptic operator are discussed.
Keywords: Newton's method, inverse iterations, tuning, invariant subspace, spectral projector. 
@article{VMP_2014_15_1_a11,
     author = {K. V. Demyanko and Yu. M. Nechepurenko},
     title = {Bi-Newton's method for computing spectral projectors},
     journal = {Numerical methods and programming},
     pages = {121--129},
     publisher = {mathdoc},
     volume = {15},
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     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_1_a11/}
}
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K. V. Demyanko; Yu. M. Nechepurenko. Bi-Newton's method for computing spectral projectors. Numerical methods and programming, Tome 15 (2014) no. 1, pp. 121-129. http://geodesic.mathdoc.fr/item/VMP_2014_15_1_a11/