Iteration methods for convexly constrained ill-posed problems in hilbert space

Numerical Functional Analysis and Optimization

Volumn 13, Issue 5-6, 1992, Pages 413-429

  Eicke, Bertolt ^a  

^a NONE   (Germany)

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[No Author keywords available]

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EID: 84880683689     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630569208816489     Document Type: Article

References (20)

1. A.B. Bakushinskii and A.V. Goncharskii, Iterative methods for the solution in incorrect problems (Russian). Nauka, Moscow, 1st edition, 1989.
2. J. Baumeister, Stable solution of inverse problems. Vieweg, Braunschweig, 1st edition 1987.
3. F.E. Browder and W.V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72 (1966), 571–575.
4. R.E. Bruck, Random products of contractions in metric and Banach spaces. J. Math. Anal. Appl. 88 (1982), 319–332.
5. C. De Boor, A Practical Guide to Splines. Springer, Appl. Math. Series 27, New York, 1st edition, 1978.
6. A.L. Dontchev and B.D. Kalchev, Duality and well-posedness in convex interpolation. Numer. Funct. Anal. Optim. 10 (1989), 673–689.
7. B. Eicke, Konvex-restringierte schlechtgestellte Probleme und ihre Regularisierung durch Iterationsverfahren. Thesis, Technische Universitat, Berlin, 1991.
8. B. Eicke, A.K. Louis and R. Plato, The instability of some gradient methods for ill-posed problems. Numer. Math. 58 (1990), 129–134.
9. A.K. Louis, Inverse und schlecht gestellte Probleme. B.G. Teubner, Stuttgart, 1st edition, 1989.
10. C.A., Micchelli, P.W. Smith, J. Swetits, and J.D. Ward, Constrained Lp Approximation. Constr. Approx. 1 (1985), 93–102.
11. C.A. Micchelli and F.I. Utreras, Smoothing and interpolation in a convex subset of a Hilbert space. SIAM J. Sci. Statist. Comput. 9 (1988), 728–746.
12. A. Neubauer, Tikhonov-regularization of ill-posed linear operator equations on closed convex sets. Thesis, Universität, Linz, 1986.
13. A. Neubauer, Tikhonov-regularization of ill-posed linear operator equations on closed convex sets, J. Approx. Theory 53 (1988), 304–320.
14. A. Neubauer, An a posteriori parameter choice for Tikhonov regularization in the presence of modeling error. Applied Numerical Mathematics (1988), 507–519.
15. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73 (1967), 591–597.
16. T.I. Seidman, Nonconvergence results for the application of least-squares estimation to ill-posed problems. J. Optim. Theory Appl. 30 (1980), 535–547.
17. G.M. Vainikko and A.Y. Veretennikov, Iteration procedures in ill-posed problems (Russian). Nauka, Moscow, 1st edition, 1986.
18. V.V. Vasin, Iterative methods for solving ill-posed problems with a priori information in Hilbert spaces. U.S.S.R. Comput. Math. and Math. Phys. 28 No.4 (1988), 6–13.
19. V.V. Vasin, Iterative methods for the approximate solution of ill-posed problems with a priori information and their applications. In H.W. Engl and C.W. Groetsch, editors, Inverse and Ill-Posed Problems, Proc. St. Wolfgang 1986, pp. 211–229, Academic Press, Boston, 1987.
20. E.H. Zarantonello, Projections on convex sets in Hilbert space and spectral theory. In E.H. Zarantonello, editor, Contributions to nonlinear functional analysis, Proc. Madison Wisc. 1971, pp. 237–424, Academic Press, New York, 1971.