A mollification framework for improperly posed problems

Numerische Mathematik

Volumn 78, Issue 4, 1998, Pages 549-575

  Hegland, M ^a   Anderssen, R S ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032342402     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050325     Document Type: Article

References (16)

1. Adams R.A. (1975): Sobolev spaces, Academic Press
2. Anderssen R.S., de Hoog F.R. (1984): Finite difference methods for the numerical differentiation of non-exact data, Computing 33, 259-267
3. Anderssen R.S., Jackett D.R. (1984): Linear functionals of foliage angle density, J. Austral. Math. Soc. Ser. B 25, no. 4, 431-441
4. Reinhardt H.-J., Hào D.N., Seiffarth F. (1994): Stable numerical fractional differentiation by mollification, Numer. Funct. Anal. and Optimiz. 15, 635-659
5. Friedrichs K.O. (1994): The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc. 55, 132-151
6. Gilbarg D., Trudinger N.S. (1983): Elliptic partial differential equations of second order, Springer
7. Groetsch C.W. (1984): The theory of Tikhonov regularization for Fredholm equations of the first kind, Pitman
8. Hille E., Phillips R.S. (1985): Functional analysis and semi-groups, American Mathematical Society, 1957, reprinted
9. Louis A.K., Maass P. (1990): A mollifier method for linear operator equations of the first kind, Inverse Problems 6, no. 3, 427ff
10. Lukas M.A. (1980): Regularization, Application and numerical solution of integral equations (Proc. Sem., Australian Nat. Univ., Canberra, 1978), Monographs Textbooks Mech. Solids Fluids: Mech. Anal., vol. 6, Nijhoff, The Hague, pp. 151-182
11. Manselli P., Miller K. (1980): Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side, Ann. Math. Pura Appl. 123, 161-183
12. Marti J.T. (1986): Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems, Academic Press
13. Murio D.A. (1987): Automatic numerical differentiation by discrete mollification, Comput. Math. Applic. 13, 381-386
14. Natterer F. (1986): The mathematics of computerized tomography, Wiley
15. Schoenberg I.J. (1973): Cardinal spline interpolation, SIAM
16. Vasin V.V. (1973): The stable evaluation of a derivative in space C(-∞,∞), USSR Comput. Math. Math. Phys. 13, 16-24