I. KNOWLES, R. WALLACE, "A variational method for numerical differentiation", Numer. Math. 70: 91-110 (1995), Numerische Mathematik c Springer-Verlag 1995.
Copyright - [Précédente] [Première page] [Suivante] - Home

Article : [ART361]

Titre : I. KNOWLES, R. WALLACE, A variational method for numerical differentiation, Numer. Math. 70: 91-110 (1995), Numerische Mathematik c Springer-Verlag 1995.

Auteur : Ian Knowles
Auteur : Robert Wallace - Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

Lien : private/KNOWLES1.pdf - 248 Ko, 20 pages.
Info : Received August 2, 1993 / Revised version received February 28, 1994
Info : Mathematics Subject Classification (1991): Primary 65D25; secondary 49M10, 34A55, 34B24

Summary : A new method is given for effecting numerical differentiation by means
of an optimization procedure. The method is shown to be effective for the differenti-ation
of noisy functions, and stability and convergence results for a steepest descent
implementation are proved.



References : 37
1. Anderssen, R.S., Bloomfield, P. (1972): On The Numerical Differentiation of Data. Technical Report No. 13, Series 2, Department of Statistics, Fine Hall, Princeton University,
2. Anderssen, R.S., Bloomfield, P. (1973/74): Numerical differentiation procedures for non-exact data. Numer. Math. 22, 157–182
3. Babu¡ ska, I., Pr´ ager, M., Vit´ asek, E. (1966): Numerical Processes in Differential Equations. Interscience Publishers, New York
4. Belaya, N.I., Ivanov, V.V. (1985): Algorithms for reconstruction of derivatives of functions of certain classes, which are optimal with respect to accuracy. Zh. v— ychisl. Mat. i mat. Fiz. 25(3), 456–461
5. Coppel, W.A. (1971): Disconjugacy. Springer, Berlin
6. Cullum, J. (1971): Numerical differentiation and regularization. SIAM J. Numer. Analysis 8(2), 254-265
7. Curry, H.B. (1944): The method of steepest descent for non-linear Minimization Problems. Quarterly App. Math. 2, 258–261
8. Demidovich, V.B. (1967): The restoration of a function and its derivative on the basis of experimental data. V— ychisl. metody i programmirovanie 8, 96–102
9. Dolgopolova, T.F. (1970): Finite dimensional regularization in the case of numerical differentiation of periodic functions. Matem. zap. Ural’skii un-t 7(4)
10. Dolgopolova, T.F., Ivanov, V.K. (1966): Numerical differentiation. Comp. Math and Math. Physics 6(3), 570–576
11. Dorofeev, I.F. (1977) On stable algorithms concerning numerical differentiation and the numerical solution of some inverse problems for equations with deviating argument, volume 15 of Colloq. Math. Soc. J´ anos Bolyai, pp. 143–154. North-Holland Amsterdam
12. Dunford, N., Schwartz, J.T. (1958): Linear Operators, volume II of Pure and Applied Mathematics. Interscience/Wiley, New York
13. Engels, H. (1973): ¨ Uber ein numerisches Differentiationsverfahren mit ableitungsfreien Fehler-schranken. Z. Angew. Math. Mech. 53, T184–T185
14. Fox, L., Mayers, D.F. (1987): Numerical Solution of Ordinary Differential Equations. Chapman & Hall, London
15. Elena Fr¢ atil¢ a (1970): A statistical method for numerical differentiation. Stud. Cerc. Mat. 22, 443–446
16. Gerlach, W. (1974): Nachkorrektur bei numerischer Differentiation. Z. Angew. Math. Mech. 54, 193
17. Goldstein, A.A. (1965): On steepest descent. SIAM J. Control 3, 147-151
18. Grabar, L.P. (1967): Numerical differentiation by means of Chebyshev polynomials orthonormalized on a system of equidistant points. Zh. v— ychisl. Mat. i mat. Fiz. 7(6), 1375–1379
19. Hartman, P. (1964): Ordinary Differential Equations. John Wiley & Sons, New York
20. Kala¡ida, A.F., Chirikalov, V.A. (1984): Approximation of the zero rank of a superposition of functions, and matrix algorithms of numerical differentiation. Vychisl. Prikl. Mat. (Kiev) 52, 10–17
21. Kolpakova, ` E.V. (1976): Numerical solution of the problem of reconstructing the derivative. Differ-necial’nye Uravnenija i Vy¢ cisl. Mat. Vyp. 6, 137–143
22. Markov, S. (1975): Computation of the derivatives of a function on the basis of its experimentally measured values. Automat. i Iz¢ cisl. Tehn. 9, 5–11
23. Miel, G., Mooney, R. (1985): On the condition number of Lagrangian numerical differentiation. Appl. Math. Comput. 16(3), 241–252
24. Neuberger, J.(1981): Steepest descent for systems of non-linear partial differential equations. Oak Ridge National Laboratory, CSD/TM-161
25. Neuberger, J. (1983): Steepest descent for general systems of linear differential equations in Hilbert spaces. Springer Lecture Notes, vol. 1032
26. Neuberger, J. (1985): Steepest descent and differential equations. J. Math. Soc. Japan 37, 85
27. Pallaghy, C.K., L¨ uttge, U. (1970): Light-induced and H + -ion uxes and bioelectric phenomena in mesophyll cells of Atriplex spongiosa. Zeit. f ¨ ur P anz. 62, 417–425
28. Sakalauskas, ` E. I. (1984): The Galerkin-Tikhonov method of regularization in the problem of numerical differentiation. Zh. v— ychisl. Mat. i mat. Fiz 11, 1742–1747
29. Surova, N.S. (1979): An investigation of the problem of reconstructing a derivative by using an optimal regularizing integral operator. Numerical methods and programming 1, 30–34. Saratov. Gos. Univ., Saratov
30. Tikhonov, A.N. (1963): On the regularization of ill-posed problems. Doklady Akad. Nauk SSSR 153(1), 49–52
31. Tikhonov, A.E., Arsenin, V.Y. (1977): Solutions of Ill-posed Problems. John Wiley & Sons, New York
32. Vandergraft, J. (1983): Introduction to Numerical Computation. Academic Press, New York
33. Vasin, V.V. (1969): Regularization of the problem of numerical differentiation. Matem. zap. Ural’skii un-t 7(2), 29–33
34. Vasin, V.V. (1973): The stable evaluation of a derivative in C(
35. Vershinin, V.V., Pavlov, N.N. (1983): Approximation of derivatives by smoothing splines. Vychisl. Sistemy 98, 83–91
36. Voronenok, E.Ja. (1972): A numerical method of inverse Laplace transformation. Zh. v¯ ychisl. Mat. i mat. Fiz. 12, 1308–1312
37. Zeidler, E. (1986): Variational Methods and Optimization, volume III of Nonlinear Functional Analysis and its Applications. Springer, New York

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.