A numerical differentiation method and its application to reconstruction of discontinuity

Inverse Problems

Volumn 18, Issue 6, 2002, Pages 1461-1476

  Wang, Yan Bo ^a   Jia, X Z ^a   Cheng, J ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DIFFERENTIATION (CALCULUS); INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

TIKHONOV REGULARIZATIONS;

INVERSE PROBLEMS;

EID: 0036905596     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/18/6/301     Document Type: Article

References (21)

1. Adams R.A. 1975 Sobolev spaces Pure and Applied Mathematics vol 65 (New York: Academic).
2. Cheng J. and Yamamoto M. 2000 One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization Inverse Problems 16 L31-8.
3. Deans S.R. 1983 Radon Transform and its Applications (New York: Wiley-Interscience).
4. Engl H.W., Hanke M. and Neubauer A. 1996 Regularization of Inverse Problems (Dordrecht: Kluwer).
5. Gautschi W. 1997 Numerical Analysis. An Introduction (Boston, MA: Birkhauser).
6. Gorenflo R. and Vessella S. 1991 Abel Integral Equations, Analysis and Applications (Springer Lecture Notes in Mathematics vol 1461) (Berlin: Springer).
7. Groetsch C.W. 1984 The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Research Notes in Mathematics vol 105) (Advanced Publishing Program) (Boston, MA: Pitman).
8. Groetsch C.W. 1991 Differentiation of approximately specified functions Am. Math. Mon. 98 847-50.
9. Hammerlin G. and Hoffmann K.H. 1991 Numerical Mathematics (New York: Springer).
10. Hanke M. and Scherzer O. 2001 Inverse problems light: numerical differentiation Am. Math. Man. 108 512-21.
11. Hegland M. 1998 Resolution enhancement of spectra using differentiation Preprint Australian National University.
12. Jia X.Z. and Wang Y.B. 2002 The numerical differentiation of the nonsmooth functions Preprint Fudan University, Shanghai.
13. Murio D.A. 1993 The Mollification Method and the Numerical Solution of Ill-Posed Problems (New York: Wiley-Interscience).
14. Natterer F. 1986 The Mathematics of Computerized Tomography (Stuttgart: Teubner).
15. Ramm A.G. 2000 Inequalities for the derivatives Math. Inequal. Appl. 3 129-32.
16. Ramm A.G. and Smirnova A.B. 2001 On stable numerical differentiation Math. Comput.. 70 1131-53.
17. Reinsch C.H. 1967 Smoothing by spline functions Numer. Math. 10 177-83.
18. Schumaker L.L. 1981 Spline Functions: Basic Theory (New York: Wiley).
19. Schoenberg I.J. 1964 Spline functions and the problem of graduation Proc. Natl Acad. Sci. USA 52 947-50.
20. Strang G. and Fix G.J. 1973 An Analysis of the Finite Element Method (Englewood Cliffs, NJ: Prentice-Hall).
21. Tikhonov A.N. and Arsenin V.Y. 1977 Solutions of Ill-Posed Problems (Washington, DC: Winston).