Geodesic
Optimal recovery and finite-dimensional approximation in linear inverse problems
Sbornik. Mathematics, Tome 199 (2008) no. 12, pp. 1735-1750 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper considers applications of the Lagrange principle to optimal recovery in a linear inverse problem with a priori information about its solution and extends previous results of the author on optimal recovery and finite-dimensional approximation. A theorem on general optimal recovery methods for problems in finite- and infinite-dimensional spaces is established and the approximation of a problem in an infinite-dimensional space by problems in finite-dimensional spaces is investigated. Applications of the theory presented are illustrated by examples. Bibliography: 11 titles. 
@article{SM_2008_199_12_a0,
     author = {A. V. Bayev},
     title = {Optimal recovery and finite-dimensional approximation in linear inverse problems},
     journal = {Sbornik. Mathematics},
     pages = {1735--1750},
     year = {2008},
     volume = {199},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_12_a0/}
}
TY  - JOUR
AU  - A. V. Bayev
TI  - Optimal recovery and finite-dimensional approximation in linear inverse problems
JO  - Sbornik. Mathematics
PY  - 2008
SP  - 1735
EP  - 1750
VL  - 199
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2008_199_12_a0/
LA  - en
ID  - SM_2008_199_12_a0
ER  - 
%0 Journal Article
%A A. V. Bayev
%T Optimal recovery and finite-dimensional approximation in linear inverse problems
%J Sbornik. Mathematics
%D 2008
%P 1735-1750
%V 199
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2008_199_12_a0/
%G en
%F SM_2008_199_12_a0
A. V. Bayev. Optimal recovery and finite-dimensional approximation in linear inverse problems. Sbornik. Mathematics, Tome 199 (2008) no. 12, pp. 1735-1750. http://geodesic.mathdoc.fr/item/SM_2008_199_12_a0/

[1] A. A. Melkman, C. A. Micchelli, “Optimal estimation of linear operators in Hilbert spaces from inaccurate data”, SIAM J. Numer. Anal., 16:1 (1979), 87–105 | DOI | MR | Zbl

[2] J. F. Traub, H. Woźniakowski, A general theory of optimal algorithms, Academic Press, New York–London, 1980 | MR | MR | Zbl | Zbl

[3] V. V. Arestov, “Optimal recovery of operators, and related problems”, Proc. Steklov Inst. Math., 189 (1990), 1–20 | MR | Zbl

[4] C. A. Micchelli, T. J. Rivlin, “Lectures on optimal recovery”, Numerical analysis (Lancaster, 1984), Lecture Notes in Math., 1129, Springer-Verlag, Berlin–Heidelberg, 1985, 21–93 | DOI | MR | Zbl

[5] G. G. Magaril-Il'yaev, K. Yu. Osipenko, V. M. Tikhomirov, “Optimal recovery and extremum theory”, Comput. Methods Funct. Theory, 2:1 (2002), 87–112 | MR | Zbl

[6] G. G. Magaril-Il'yaev, V. M. Tikhomirov, Convex analysis: theory and applications, Transl. Math. Monogr., 222, Amer. Math. Soc., Providence, RI, 2003 | MR | Zbl

[7] A. V. Baev, “Printsip Lagranzha i konechnomernaya approksimatsiya v zadache optimalnogo obrascheniya lineinykh operatorov”, Vych. metody i programmirovanie, 7:2 (2006), 323–336 ; http://www.srcc.msu.su/num-meth

[8] G. G. Magaril-Il'yaev, K. Yu. Osipenko1, “Optimal recovery of functionals based on inaccurate data”, Math. Notes, 50:6 (1991), 1274–1279 | DOI | MR | Zbl | Zbl

[9] N. Dunford, J. T. Schwartz, Linear operators. I. General theory., Pure Appl. Math., 7, Intersci. Publ., New York–London, 1958 | MR | MR | Zbl

[10] A. V. Bayev, “The Lagrange principle in the problem of optimal inversion of linear operators in finite-dimensional spaces with a priori information about its solution”, Comput. Math. Math. Phys., 47:9 (2007), 1452–1463 | DOI | MR

[11] A. V. Bayev, A. G. Yagola, “Optimal recovery in problems of solving linear integral equations with a priori information”, J. Inverse Ill-Posed Probl., 15:6 (2007), 569–586 | DOI | MR | Zbl