On convergence of approximations in the regularization method and the Tikhonov regularization method on the n-th order

Journal of Inverse and Ill-Posed Problems

Volumn 6, Issue 3, 1998, Pages 243-262

  Menikhes, L D ^a   Tanana, V P ^b  

^a SOUTH URAL STATE UNIVERSITY   (Russian Federation)

^b CHELYABINSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644325611     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/jiip.1998.6.3.243     Document Type: Article

References (11)

1. A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, Finite difference approximation of linear ill-posed problems. J. of Calc. Math, and Math. Phys. (1974) 14, No. 1, 15–24 (in Russian).
2. V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and its Applications. Nauka, Moscow, 1978 (in Russian).
3. L. D. Menikhes and V. P. Tanana, A convergence criterion for approximations in the residual method in Banach spaces. Journal of Inverse and Ill-Posed Problems (1997) 5, No. 3, 255–264.
4. V. P. Tanana, Methods of Solution of Operator Equations. Nauka, Moscow, 1981 (in Russian).
5. V. P. Tanana, Finite-dimensional approximation of the regularization method when solving inverse problems. Dokl. Akad. Nauk SSSR (1984) 277, No. 3, 557–559 (in Russian).
6. V. P. Tanana, Finite-dimensional approximation of the regularization method. Izv. Vuzov, Mathematics (1986) 7, 65–69 (in Russian).
7. A. N. Tikhonov, On regularization of ill-posed problems. Dokl. Akad. Nauk SSSR (1963) 153, No.l, 49–52 (in Russian).
8. A. N. Tikhonov, On solution of ill-posed problems and the regularization method. Dokl. Akad. Nauk SSSR (1963) 151, No. 3, 501–504 (in Russian).
9. V. V. Vasin and V. P. Tanana, Necessary and sufficient conditions of convergence of projection methods for unstable problems. Dokl. Akad. Nauk SSSR (1974) 215, No. 5, 1032–1034 (in Russian).
10. V. V. Vasin, Discrete convergence and finite-dimensional approximation of regularizing algorithms. Journ. of Calc. Math, and Math. Phys. (1979) 19, No. 1, 11–21 (in Russian).
11. V.V. Vasin, Methods of Solution of Unstable Problems. Izd. Ural Gos. Univ., Sverdlovsk, 1989 (in Russian).