Geodesic
Convergence of the Newton--Kantorovich Method for Calculating Invariant Subspaces
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 109-114

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We propose a version of the Newton–Kantorovich method which, given a nondegenerate square $n\times n$ matrix and a number $m$, allows us to calculate the invariant subspace corresponding to its smallest (in modulus) eigenvalues. We obtain estimates of the rate of convergence via an integral criterion for circular dichotomy. 
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     author = {Yu. M. Nechepurenko and M. Sadkane},
     title = {Convergence of the {Newton--Kantorovich} {Method} for {Calculating} {Invariant} {Subspaces}},
     journal = {Matemati\v{c}eskie zametki},
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Yu. M. Nechepurenko; M. Sadkane. Convergence of the Newton--Kantorovich Method for Calculating Invariant Subspaces. Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 109-114. http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a9/