Inverse problems light: Numerical differentiation

American Mathematical Monthly

Volumn 108, Issue 6, 2001, Pages 512-521

  Hanke Bourgeois, Martin ^a   Scherzer, Otmar ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035374241     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.1080/00029890.2001.11919778     Document Type: Article

References (13)

1. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Kluwer, Dordrecht, 1996.
2. C.W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, London, 1984.
3. _, Differentiation of approximately specified functions, Amer. Math. Monthly 98 (1991) 847-850.
4. _, Inverse Problems in the Mathematical Sciences, Vieweg, Braunschweig, 1993.
5. G. Hämmerlin and K.-H. Hoffmann, Numerical Mathematics, Springer-Verlag, New York, 1991.
6. M. Hanke and O. Scherzer, Error analysis of an equation error method for the identification of the diffusion coefficient in a quasilinear parabolic differential equation. SIAM J. Appl. Math. 59 (1999) 1012-1027.
7. D.A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems, Wiley, New York, 1993.
8. C.H. Reinsch, Smoothing by spline functions, Numer. Math. 10 (1967) 177-183.
9. J. Rice and M. Rosenblatt, Smoothing splines: regression, derivatives and deconvolution, Ann. Stat. 52 (1964) 141-156.
10. I.J. Schoenberg, Spline functions and the problem of graduation, Proc. Nat. Acad. Sci. USA 52 (1964) 947-950.
11. L.L. Schumaker, Spline Functions: Basic Theory, Wiley. New York. 1981.
12. G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973.
13. G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, 1990.