×

zbMATH — the first resource for mathematics

On the Ahlberg-Nilson extension of spline interpolation: The \(g\)-splines and their optimal properties. (English) Zbl 0159.08401

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Schoenberg, I.J, On monosplines of least deviation and best quadrature formulae, SIAM J. num. anal., 2, 144-170, (1965) · Zbl 0136.36203
[2] Schoenberg, I.J, On best approximation of linear operators, Indag. math., 26, 155-163, (1964) · Zbl 0146.08501
[3] Sard, A, Linear approximation, Math. surveys no. 9, (1963), Providence, Rhode Island · Zbl 0115.05403
[4] Ahlberg, J.H; Nilson, E.N, The approximation of linear functionals, SIAM J. num. anal., 3, 173-182, (1966) · Zbl 0147.05102
[5] Birkhoff, G.D, General Mean value and remainder theorems with applications to mechanical differentiation and integration, Trans. amer. math. soc., 7, 107-136, (1906) · JFM 37.0308.02
[6] Greville, T.N.E, Spline functions, interpolation and numerical quadrature, (), A chapter in · Zbl 0312.65007
[7] Curry, H.B; Schoenberg, I.J, On polya frequency functions IV: the fundamental spline functions and their limits, J. anal. math., 17, 71-107, (1966) · Zbl 0146.08404
[8] Schoenberg, I.J; Schoenberg, I.J, On spline functions, (), (1966), to appear in · Zbl 0156.28702
[9] Marsden, M; Schoenberg, I.J, On variation diminishing spline approximation methods, Mathematica (cluj), 8, 61-82, (1966) · Zbl 0171.31001
[10] Hermite, Ch, Sur la formule d’interpolation de Lagrange, J. reine angew. math., 84, 70-79, (1878) · JFM 09.0312.02
[11] Oeuvres, Vol. 3, 432-443.
[12] Polya, G, Bemerkungen zur interpolation und zur Näherungstheorie der balkenbiegung, Z. angew. math. mech., 11, 445-449, (1931) · JFM 57.1058.01
[13] Schoenberg, I.J, On Hermite-Birkhoff interpolation, J. math. anal. appl., 16, 538-543, (1966) · Zbl 0156.28702
[14] Lidstone, G.J, Notes on the extension of Aitken’s theorem, (), 16-19 · JFM 56.1053.03
[15] Boas, R.P; Buck, R.C, Polynomial expansions of analytic functions, (), 2nd printing corrected · Zbl 0116.28105
[16] Whittaker, J.M, Sur LES séries de base de polynomes quelconques, (1949), Gauthier-Villars Paris · Zbl 0038.22804
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.