On converse and saturation results for tikhonov regulartzatton of linear ill-posed problems

SIAM Journal on Numerical Analysis

Volumn 34, Issue 2, 1997, Pages 517-527

  Neubauer, Andreas ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Converse and saturation results; Linear ill posed problems; Tikhonov regularization

Indexed keywords

EID: 0004865563     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142993253928     Document Type: Article

References (10)

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 (1988), pp. 395-417.
2. H. GFRBRER, An a-posteriori parameter choice for ordinary and iterated Tikhonov regulariza- tion of ill-posed problems leading to optimal convergence rates, Math. Comp., 49 (1987), pp. 507-522, 535-S12.
3. C. W. GROETSCH, The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind, Pitman, Boston, MA, 1984.
4. C. W. GROETSCH AND A. NEUBAUER, Regularization of ill-posed problems: Optimal parameter choice in finite dimensions, J. Approx. Theory, 56 (1989), pp. 184-200.
5. M. HANKE, Accelerated Landweber iterations for the solution of ill-posed equations, Numer. Math., 60 (1991), pp. 341-373.
6. J. T. KING AND A. NEUBAUER, A variant of finite-dimensional Tikhonov regularization with a-posteriori parameter choice, Computing, 40 (1988), pp. 91-109.
7. A. NEUBAUER, Tikhonov-Regularization of Ill-Posed Linear Operator Equations on Closed Convex Sets, Ph.D. thesis, Department of Mathematics, University of Linz, Austria, 1985.
8. T. RAUS, On the discrepancy principle for the solution of ill-posed problems, Uch. Zap. Tartu Gos, Univ., 672 (1984), pp. 16-26. (In Russian.)
9. T. RAUS, On the residue principle for the solution of ill-posed problems with non-selfadjoint operator, Uch. Zap. Tartu Gos. Univ., 715 (1985), pp. 12-20. (In Russian.)
10. E. SCHOCK, Approximate solution of ill-posed equations: Arbitrarily slow convergence vs. su- perconvergence, in Constructive Methods for the Practical Treatment of Integral Equations, G. Hämmerlin and K. H. Hoffmann, eds., Birkhäuser, Basel, 1985, pp. 234-243.