On spline regularized inversion of noisy Laplace transforms

Journal of Computational and Applied Mathematics

Volumn 83, Issue 1, 1997, Pages 39-54

  Iqbal, M ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Convolution equation; Cross validation; Filter function; Ill posed problem; Inversion of Laplace transform; Spline regularization; System theory

Indexed keywords

APPROXIMATION THEORY; INTEGRAL EQUATIONS; INVERSE PROBLEMS; PERTURBATION TECHNIQUES; SYSTEM THEORY;

CONVOLUTION EQUATION; SPLINE REGULARIZATION;

LAPLACE TRANSFORMS;

EID: 0031223159     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00028-9     Document Type: Article

References (24)

1. P. Brianzi, A criterion for the choice of a sampling parameter in the problem of Laplace transform inversion, Inverse Problems 10 (1994) 55-61.
2. P. Brianzi, M. Frontini, On the regularized inversion of the Laplace transform, Inverse Problems 7 (1991) 355-368.
3. D.E. Chauveau et al., Regularized inversion of noisy Laplace transforms, Adv. Appl. Math. 15 (1994) 186-201.
4. C. Cristina et al., Use of Laguerre functions in the inversion of Laplace transform, Inverse Problems 9 (1993) 57-68.
5. B. Davies, B. Martin, Numerical inversion of the Laplace transform, J. Comput. Phys. 33 (2) (1979) 1-32.
6. W.A. Essah, L.M. Delves, On the numerical inversion of the Laplace transform, Inverse Problems 4 (1988) 705-724.
7. W. Gautschi, Attenuation factors in practical Fourier analysis, Numer. Math. 18 (1972) 373-400.
8. G. Giunta et al., More on the Weeks method for the numerical inversion of the Laplace transform, Numer. Math. 54 (1988) 193-200.
9. N.P. Jewell, Mixtures of exponential distributions, Ann. Statist. 10 (1982) 479-484.
10. 6.
11. J.G. McWhirter, E.R. Pike, On the numerical inversion of the Laplace transform and similar FI equations of the first kind, J. Phys. A 11 (9) (1978) 1729-1745.
12. H.V. Nordan, Numerical inversion of Laplace transform, Acta Acad. Abo. 22 (1981) 3-31.
13. N. Ostrowski et al., Exponential sampling method for light scattering poly-disperity analysis, Optica Acta 28 (1981) 1059-1070.
14. A. Papoulis, A new method of inversion of Laplace transform, Quart. Appl. Maths. 14 (1956) 405-414.
15. L.L. Pennisi, Elements of Complex Variables, McGraw-Hill, New York, 1976.
16. R. Piessens, Laplace transform inversion, J. Comput. Appl. Math. 1 (1975) 115-128.
17. R. Piessens, M. Branders, Numerical inversion of the Laplace transform using generalized Laguerre polynomials, Proc. IEE 118 (1971) 1517-1522.
18. H.E. Salzer, Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transform, Math. Tables and Other Aids to Comput. 9 (1955) 164-177; also J. Math. Phys. 37 (1958) 80-108.
19. H.E. Salzer, Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transform, Math. Tables and Other Aids to Comput. 9 (1955) 164-177; also J. Math. Phys. 37 (1958) 80-108.
20. J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Springer, Berlin (1978).
21. A. Talbot, The accurate numerical inversion of Laplace transforms, J. Inst. Math. Appl. 23 (1) (1979) 97-120.
22. A.N. Tikhonov, V.Y. Arsenin, Solution of ill-posed Problems (translated from the Russian), Wiley, New York, 1977.
23. J.M. Varah, Pitfalls in the numerical solution of linear ill-posed problems, SIAM J. Sci. Statist. Comput. 4 (2) (1983) 164-176.
24. G. Wahba, Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal. 14 (1977) 651-677.