Some results and a conjecture on the degree of ill-posedness for integration operators with weights

Inverse Problems

Volumn 21, Issue 2, 2005, Pages 427-433

  Hofmann, Bernd ^a   Von Wolfersdorf, Lothar ^b  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^b TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; INTEGRATION; INVERSE PROBLEMS; ITERATIVE METHODS; LINEAR EQUATIONS; MAPPING; PROBLEM SOLVING; SET THEORY;

INTEGRATION OPERATORS; LINEAR OPERATORS; MULTIPLICATION OPERATORS; WEIGHT FUNCTIONS;

MATHEMATICAL OPERATORS;

EID: 17444395614     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/2/001     Document Type: Article

References (27)

1. Baumeister J 1987 Stable Solution of Inverse Problems (Braunschweig: Vieweg)
2. Bertero M and Boccacci P 1993 An approach to inverse problems based on ε-entropy Inverse Problems: Principles and Applications in Geophysics, Technology, and Medicine ed G Anger et al (Berlin; Akademie-Verlag) pp 76-86
3. Colton D and Kress R 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Berlin: Springer)
4. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
5. Erdélyi A 1981 Higher Transcendental Functions vol II (Based, in part, on notes left by Harry Bateman) (Malabar, FL: Krieger)
6. Freitag M 2004 On the influence of multiplication operators on the ill-posedness of inverse problems Diploma Thesis Chemnitz University of Technology, Faculty of Mathematics
7. Gorenflo R and Hofmann B 1994 On autoconvolution and regularization Inverse Problems 10 353-73
8. Hein T and Hofmann B 2003 On the nature of ill-posedness of an inverse problem arising in option pricing Inverse Problems 19 1319-38
9. Hofmann B 1986 Regularization for Applied Inverse and Ill-Posed Problems (Leipzig: Teubner)
10. Hofmann B 1994 On the degree of ill-posedness for nonlinear problems J. Inv. Ill-Posed Problems 2 61-76
11. Hofmann B 1998 A local stability analysis of nonlinear inverse problems Inverse Problems in Engineering - Theory and Practice ed D Delaunay et al (New York: The American Society of Mechanical Engineers) pp 313-20
12. Hofmann B and Fleischer G 1999 Stability rates for linear ill-posed problems with compact and non-compact operators Z. Anal. Anw. 18 267-86
13. Hofmann B and Scherzer O 1994 Factors influencing the ill-posedness of nonlinear problems Inverse Problems 10 1277-97
14. Hofmann B and Tautenhahn U 1997 On ill-posedness measures and space change in Sobolev scales J. Anal. Appl. (ZAA) 16 979-1000
15. Hohage T 2000 Regularization of exponentially ill-posed problems Numer. Funct. Anal. Optim. 21 439-64
16. Jahnke-Ende 1960 Tables of Higher Functions (Leipzig: Teubner)
17. Kamke E 1961 Differentialgleichungen, Lösungsmethoden und Lösungen - I Gewöhliche Differentialgleichungen (Leipzig: Akad Verlagsges Geest & Portig)
18. Kirsch A 1996 An Introduction to the Mathematical Theory of Inverse Problems (New York: Springer)
19. Kress R 1989 Linear Integral Equations (Berlin: Springer)
20. Louis A K 1989 Inverse und schlecht gestellte Probleme (Stuttgart: Teubner)
21. Mathé P and Pereverzev S V 2003 Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803
22. Natterer F 1984 Error bounds for Tikhonov regularization in Hilbert scales Appl. Anal. 18 29-37
23. Tautenhahn U 1998 Optimality for ill-posed problems under general source conditions Numer. Funct. Anal. Optim. 19 377-98
24. Vu Kim Tuan and Gorenflo R 1994 Asymptotics of singular values of fractional integral operators Inverse Problems 10 949-55
25. Wahba G 1980 Ill-posed problems: numerical and statistical methods for mildly, moderately and severely ill-posed problems with noisy data Technical Report no 595 University of Wisconsin, Madison
26. Wing G M 1985 Condition numbers of matrices arising from the numerical solution of linear integral equations of the first kind J. Integral Eqns 9 (Suppl.) 191-204
27. Zabrejko P P et al 1975 Integral Equations - A Reference Text (Leyden: Noordhoff)