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Sur le choix du paramètre d’ajustement dans le lissage par fonctions spline. (French) Zbl 0414.65007

MSC:
65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
41A15 Spline approximation
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References:
[1] Ahlberg, J.H., Nilson, E.N., Walsh: The theory of splines and their applications. New-York: Academic (1967) · Zbl 0158.15901
[2] Chatelin, F., Lemordant, J.: La m?thode de Rayleigh-Ritz appliqu?e ? des op?rateurs diff?rentiels elliptiques, ordres de convergence des ?l?ments propres. Numer. Math.23, 215-222 (1975) · Zbl 0295.65060
[3] Courant, R., Hilbert, D.: Methods of Mathematical Physics, New-York: Interscience Publishers (1953) · Zbl 0051.28802
[4] Craven, P., Wahba, G.: Smoothing noisy data with spline functions estimating the correct degree of smoothing by the method of generalized cross-validation. TR#445 (october 1977) University of Winsconsin-Madison · Zbl 0377.65007
[5] Fix, G.: Effects of quadrature errors in finite element approximation of steady state, eigenvalue and parabolic problems. In: Foundations of the finite element method with applications to partial differential equations. A.K. Aziz, ed. New York: Academic (1972) · Zbl 0282.65081
[6] Joly, J.L.: Th?or?mes de convergence pour les fonctions spline g?n?rales d’interpolation et d’ajustement. C.R. Acad. Sci. Paris 264, ser. A. 126-128 (1970)
[7] Laurent, P.J.: Approximation et optimisation. Paris: Hermann (1972) · Zbl 0238.90058
[8] Necas, J.: Les m?thodes directes en th?orie des equations elliptiques. Paris: Masson (1967)
[9] Paihua, L.: Quelques m?thodes num?riques pour le calcul de fonctions spline ? une et plusieurs variables. Th?se, Universit? Scientifique et M?dicale de Grenoble Grenoble (Mai 1978)
[10] Robert, F.: Analyse num?rique it?rative. Cours I.N.P.G. Grenoble (1974)
[11] Stone, M.: Cross-validatory choice and assesement of statistical prediction. J. Roy. Statist. Soc. Ser. B,36, 111-147 (1974) · Zbl 0308.62063
[12] Sutti, C., One dimensional minimisation methods. In: Minimisation algorithms. G.P. Szeg?, ed. London: Academic (1972)
[13] Wahba, G., Wold, S.: A completely automatic french curve: fitting spline functions by crossvalidation. Commun. Statist.4, 1-17 (1975) · Zbl 0305.62043
[14] Wahba, G.: A survey of some smoothing problems and the method of generalized crossvalidation for solving them. TR#457 (July 1976) University of Wisconsin-Madison
[15] Wahba, G.: Smoothing Noisy Data with Spline Functions. Numer. Math.24, 383-393 (1975) · Zbl 0299.65008
[16] Wahba, G.: Optimal smoothing of density estimates. TR#469 (october 1976), University of Wisconsin-Madison · Zbl 0329.65040
[17] Wahba, G.: Practical approximate solutions to linear operator equations when the data are noisy. SIAM, J. Num. Analysis.14, 4 (1977) · Zbl 0402.65032
[18] Weinberger, H.F.: Variational methods for eigenvalue approximations. SIAM, Philadelphia (1974) · Zbl 0296.49033
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