A.G. RAMM, A.B. SMIRNOVA, "ON STABLE NUMERICAL DIFFERENTIATION", MATHEMATICS OF COMPUTATION, Volume 00, Number 0, Xxxx XXXX, Pages 000-000.
Copyright - [Précédente] [Première page] [Suivante] - Home

Article : [ART360]

Titre : A.G. RAMM, A.B. SMIRNOVA, ON STABLE NUMERICAL DIFFERENTIATION, MATHEMATICS OF COMPUTATION, Volume 00, Number 0, Xxxx XXXX, Pages 000-000.

Auteur : ALEXANDER G. RAMM
Auteur : ALEXANDRA B. SMIRNOVA

Source : MATHEMATICS OF COMPUTATION
Volume : 00
Number : 0, Xxxx XXXX
Pages : 000 - 000
S : 0025-5718(XX)0000-0
Lien : private/RAMM1.pdf - 281 Ko, 20 pages.

Abstract : A new approach to the construction of fnite-difference methods
is presented. It is shown how the multi-point differentiators can generate reg-
ularizing algorithms with stepsize h being a regularization parameter. The
explicitly computable estimation constants are given. Also an iteratively reg-
ularized scheme for solving the numerical differentiation problem in the form
of Volterra integral equation is developed.

References
1. R.G.Airapetyan, A.G.Ramm, A.B.Smirnova, Continuous methods for solving nonlinear illposed problems, in the book "Operator theory and applications", Amer. Math. Soc., Fields Institute Communications, Providence,RI, 2000, pp. 111-138.
2. R.S.Anderssen, P.Bloomfield, Numerical differentiation procedures for non-exact data, Numer. Math. 22 (1973/74), 157-182.
3. R.S.Anderssen, F.R.de Hoog, Finite difference methods for the numerical differentiation of non-exact data, Computing. 33 (1984), 259-267.
4. J.Cullum, Numerical differentiation and regularization, SIAM J. Numer. Analysis. 8(2)(1971), 254-265.
5. T.F.Dolgopolova, Finite dimensional regularization in the case of numerical differentiation of periodic functions, Matem. zap. Ural'skii un-t. 7(4) (1970), 27-33.
6. T.F.Dolgopolova, V.K.Ivanov, Numerical differentiation, Comp. Math and Math. Physics.6(3) (1966), 570-576.
7. Yu.V.Egorov, V.A.Kondrat'ev, On a problem of numerical differentiation, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 3 (1989), 80-81.
8. V.K.Ivanov, On linear ill-posed problems, Doklady Akad. Nauk SSSR. 145(2) (1962), 270-272.
9. I.Knowles, R. Wallace, A variational method for numerical differentiation, Numer. Math. 70 (1995), 91-110.
10. E.V.Kolpakova, Numerical solution of the problem of reconstructing the derivative, differencial'nye Uravnenija i Vychisl. Mat. 6 (1976), 137-143.
11. C.Lanczoc, Applied Analysis, Englewood Cli s, N.J. Prentice-Hall, 1956.
12. T.Miller, A. G.Ramm, Estimates of the derivatives of random functions II, J. Math. Anal. Appl. 110 (1985), 429-435.
13. C.K. Pallaghy, U.Luttge, Light-induced and H-ion uxes and bioelectric phenomena in mesophyll cells of Atriplex Spongiosa, Zeit. fuer P anz. 62 (1970), 417-425.
14. D.L. Phillips, A technique for the numerical solution of certain integral equation of the first kind, J. Assoc. Comput. Machinery. 9(1) (1962), 84-97.
15. R.Qu, A new approach to numerical differentiation and regularization, Math. Comput. Modelling. 24(10) (1996), 55-68.
16. A.G.Ramm, On numerical differentiation, Mathem., Izvestija vuzov, 11 (1968), 131-135.
17. , Simplified optimal differentiators, Radiotech.i Electron. 17 (1972), 1325-1328.
18. , On simultaneous approximation of a function and its derivative by interpolation polynomials, Bull. Lond. Math. Soc. 9 (1977), 283-288.
19. , Stable solutions of some ill-posed problems, Math. Meth. in appl. Sci. 3 (1981), 336-363.
20. , Estimates of the derivatives of random functions, J. Math. Anal. Appl., 102 (1984), 244-250.
21. , Random fields estimation theory, Longman Scientific and Wiley, New York, 1990.
22. , Inequalities for the derivatives, Math. Ineq. and Appl., 3, N1, (2000), 129-132.
23. A.G Ramm, A.I.Katsevich, The Radon transform and local tomography, CRC Press Boca Raton, 1996.
24. T.J.Rivlin, Optimally stable Lagrangian numerical differentiation, SIAM J. Numer. Analysis. 12(5) (1975), 712-725.
25. H.E.Salzer, Some problems in optimally stable Lagrangian differentiation, Math. Comp. 28(1974), 1105-1115.
26. A.N.Tikhonov, V.Y.Arsenin, Solutions of ill-posed problems, John Wiley and Sons, New York,1977.
27. V.V.Vasin, Regularization of numerical differentiation problem, Matem. zap. Ural'skii un-t. 7(2) (1969), 29-33.
28. V.V.Vasin, The stable evaluation of a derivative in C(-inf, +inf), Comp. Math and Math. Physics. 13(6) (1973), 1183-1389.
29. V.V.Vasin, A.L. Ageev, Ill-poses problems with a priori information, VNU, Utercht, 1995.


Mise à jour le lundi 10 avril 2023 à 18 h 47 - E-mail : thierry.lequeu@gmail.com
Cette page a été produite par le programme TXT2HTM.EXE, version 10.7.3 du 27 décembre 2018.

Copyright 2023 : TOP

Les informations contenues dans cette page sont à usage strict de Thierry LEQUEU et ne doivent être utilisées ou copiées par un tiers.
Powered by www.google.fr, www.e-kart.fr, l'atelier d'Aurélie - Coiffure mixte et barbier, La Boutique Kit Elec Shop and www.lequeu.fr.