Geodesic
Convergence of the Newton–Kantorovich Method for Calculating Invariant Subspaces
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 109-114 
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/
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     title = {Convergence of the {Newton{\textendash}Kantorovich} {Method} for {Calculating} {Invariant} {Subspaces}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Godunov S. K., Sadkane M., Robbe M., “Smoothing techniques and computation of invariant subspaces of elliptic operators”, Appl. Numerical Math., 33 (2000), 341–347 | DOI | MR | Zbl

[2] Godunov S. K., Nechepurenko Yu. M., “Otsenki skorosti skhodimosti metoda Nyutona dlya vychisleniya invariantnykh podprostranstv”, ZhVM i MF, 42:6 (2002), 771–779 | MR | Zbl

[3] Bulgakov A. Ya., Godunov S. K., “Krugovaya dikhotomiya matrichnogo spektra”, Sib. matem. zh., 29:5 (1988), 59–70 | MR

[4] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauchnaya Kniga, Novosibirsk, 1997