Geodesic
Iterative methods for solving linear operator equations in Banach spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 303-318
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Iterative methods for solving the linear operator equation $Ax=y$ with $B$-symmetric $B$-positive operator acting from a Banach space $X$ to a Banach space $Y$ are considered. The space $X$ is assumed to be uniformly convex and smooth, whereas $Y$ is an arbitrary Banach space. The cases of exact and disturbed data are considered and the strong (norm) convergence of the iterative processes is proved.
Keywords: iterative method, duality mapping, $B$-symmetric operator, $B$-positive operator, Bregman distance, uniformly convex space, smooth space, Xu–Roach characteristic inequality, modulus of smoothness of a space.
Mots-clés : minimum-norm solution 
@article{TIMM_2011_17_3_a30,
     author = {P. A. Chistyakov},
     title = {Iterative methods for solving linear operator equations in {Banach} spaces},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {303--318},
     year = {2011},
     volume = {17},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a30/}
}
TY  - JOUR
AU  - P. A. Chistyakov
TI  - Iterative methods for solving linear operator equations in Banach spaces
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2011
SP  - 303
EP  - 318
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a30/
LA  - ru
ID  - TIMM_2011_17_3_a30
ER  - 
%0 Journal Article
%A P. A. Chistyakov
%T Iterative methods for solving linear operator equations in Banach spaces
%J Trudy Instituta matematiki i mehaniki
%D 2011
%P 303-318
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a30/
%G ru
%F TIMM_2011_17_3_a30
P. A. Chistyakov. Iterative methods for solving linear operator equations in Banach spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 303-318. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a30/

[1] Landweber L., “An iteration formula for Fredholm integral equations of the first kind”, Am. J. Math., 73 (1951), 615–624 | DOI | MR | Zbl

[2] Schopfer F., Louis A. K., Schuster T., “Nonlinear iterative methods for linear ill-posed problems in Banach spaces”, Inverse Problems, 22 (2006), 311–329 | DOI | MR

[3] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972, 496 pp. | MR

[4] Xu Z. B., Roach G. F., “Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces”, J. Math. Anal. Appl., 157 (1991), 189–210 | DOI | MR | Zbl

[5] Cioranescu I., Geometry of Banach spaces, duality mappings, and nonlinear problems, Kluwer, Dordrecht, 1990, 260 pp. | MR | Zbl

[6] Distel Dzh., Geometriya banakhovykh prostranstv: izbrannye glavy, Vischa shkola, Kiev, 1980, 216 pp. | MR

[7] Lindenstrauss J., Tzafriry L., Classical Banach spaces, v. II, Springer-Verlag, New York–Berlin, 1979, 243 pp. | MR | Zbl