Geodesic
A regularized parameter choice in regularization for a common solution of a finite system of ill-posed equations involving Lipschitz continuous and accretive mappings
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3 
Buong Nguyen; Dinh Dung Nguyen. A regularized parameter choice in regularization for a common solution of a finite system of ill-posed equations involving Lipschitz continuous and accretive mappings. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we present a regularized parameter choice in a new regularization method of Browder–Tikhonov type, for finding a common solution of a finite system of ill-posed operator equations involving Lipschitz continuous and accretive mappings in a real reflexive and strictly convex Banach space with a uniformly Gateaux differentiate norm. An estimate for convergence rates of regularized solution is also established.

[1] E. F. Browder, “Nonlinear mapping of nonexpansive and accretive type in Banach spaces”, Trans. Am. Math. Soc., 73 (1967), 875–882 | MR | Zbl

[2] Ya. I. Alber, “On solution by the method of regularization for operator equation of the first kind involving accretive mappings in Banach spaces”, Differ. Equations SSSR, 11 (1975), 2242–2248 | MR

[3] M. Haltmeier, R. Kowar, A. Leitao, O. Scherzer, “Kaczmarz methods for nonlinear ill-posed equations. I: Convergence analysis”, Inverse Probl. Imaging, 1 (2007), 289–298 | DOI | MR | Zbl

[4] A. D. Cezaro, M. Haltmeier, A. Leitao, O. Scherzer, “On steepest-descent-Kaczmarz method for regularizing systems of nonlinear ill-posed equations”, Appl. Math. Comput., 202 (2008), 596–607 | DOI | MR | Zbl

[5] J. Baumeister, B. Kaltenbacher, A. Leitao, “On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations”, Inverse Probl. Imaging, 4 (2010), 335–350 | DOI | MR | Zbl

[6] A. D. Cezaro, J. Baumeister, A. Leitao, “Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations”, Inverse Probl. Imaging, 5 (2010), 1–17 | DOI | MR

[7] Ng. Buong, “Regularization for unconstrained vector optimization of convex functionals in Banach spaces”, Comput. Math. Math. Phys., 46 (2006), 354–360 | DOI | MR | Zbl

[8] Ng. Buong, Ng. D. Dung, “Regularization for a common solution of a system of nonlinear ill-posed equations”, Int. J. Math. Anal., 34 (2009), 1693–1699 | MR

[9] M. M. Vainberg, Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, Nauka, M., 1972 (in Russian) | MR | Zbl

[10] Ya. I. Alber, I. P. Ryazantseva, Nonlinear Ill-Posed Problems of Monotone Types, Springer, Berlin, 2006 | MR

[11] Ng. Buong, “On nonlinear ill-posed accretive equations”, Southeast Asian Bull. Math., 28 (2004), 1–6 | MR

[12] Ng. Buong, Ng. Th. H. Phuong, “Regularization method for a class of variational inequalities in Banach spaces”, Comput. Math. Math. Phys., 52 (2012), 1487–1496 | DOI

[13] Ng. Buong, Ng. Th. H. Phuong, “Regularization methods for nonlinear ill-posed equations involving $m$-accretive mappings in Banach spaces”, Russ. Math., 57 (2013), 58–64 | DOI | Zbl

[14] L. V. Kantorovich, G. P. Akilov, Functional Analysis, Pergamon, Oxford, 1982 ; Nauka, M., 1997 | MR | Zbl