zbMATH — the first resource for mathematics

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

65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
41A15 Spline approximation
Full Text: DOI EuDML
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.