On pseudo-optimal parameter choices and stopping rules for regularization methods in Banach spaces

Numerical Functional Analysis and Optimization

Volumn 17, Issue 1-2, 1996, Pages 181-195

  Plato, R ^a   Hamarik U ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF TARTU   (Estonia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000710028     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569608816690     Document Type: Article

References (12)

1. H.W. Engl and H. Gfrerer. A posteriori parameter choice for general regularization methods for solving linear ill-posed problems. Appl. Numer. Math., 4:395-417, 1988.
2. H. Gfrerer. On a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Math. Comp., 49:507-622, 1987.
3. U. Hämarik. On a parameter choice in the regularized Ritz-Galerkin method. Proc. Estonian Acad. Sci. Phys. Math., 42:133-143, 1993.
4. A.S. Leonov. On the accuracy of Tikhonov regularizing algorithms and quasioptimal selection of a regularization parameter. Soviet Math. Dokl., 44(3):711-716, 1991.
5. M.Z. Nashed. Inner, outer and generalized inverses in Danach and Hilbert spaces. Numer. Funct. Anal. Optim., 9(3-4):261-325, 1987.
6. O. Nevanlinna. Convergence of Iterations for Linear Equations. Birkhäuser, Basel, Boston, Berlin, 1st edition, 1993.
7. T. Pazy. Semigroups and Applications to Partial Differential Operators. Springer, New York, 1st, reprint edition, 1983.
8. R. Plato. The discrepancy principle for iterative and other methods to solve linear ill-posed equations. Submitted for publication.
9. R. Plato. Two iterative schemes for solving linear non-necessarily well-posed problems in Banach spaces. In A.N. Tikhonov, editor, Proc. Moscow 1991, pages 134-143, Utrecht, Tokyo, 1992. VSP.
10. R. Plato. On resolvent conditions for Abel integral operators. In preparation.
11. T. Raus. Residue principle for ill-posed problems (in Russian). Acta et comment. Univers. Tartuensis, 672:16-26, 1984.
12. T. Raus. Residue principle for ill-posed problems with nonselfadjoint operators (in Russian). Acta et comment. Univers. Tartuensis, 715:12-20, 1985.