Kobza, Jiří Spline recurrences for quartic splines. (English) Zbl 0854.41011 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 34, 75-89 (1995). Summary: The linear dependence relations for the local parameters of quartic spline (spline recurrences) are presented. The cases of splines interpolating function values at knots and midpoints, mean values and values of the first derivative are studied. The recurrences between prescribed values and values of various derivatives of the spline are given. The structure of related systems of linear equations for computing parameters of the spline is investigated. Cited in 9 Documents MSC: 41A15 Spline approximation 65D05 Numerical interpolation Keywords:spline interpolation; recurrence relations; quartic spline × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Ahlberg J. H., Nilson E. N., Walsh J. L.: The Theory of Splines and Their Applications. Academic Press, N.Y., 1967. · Zbl 0158.15901 [2] Albasiny E. L., Hoskins W. D.: The numerical calculation of odd-degree polynomial splines with equidistant knots. J. Inst. Maths. Appl. 7 (1971), 384-397. · Zbl 0217.42303 · doi:10.1093/imamat/7.3.384 [3] Boor C. de: A Practical Guide to Splines. Springer, N.Y., 1978. · Zbl 0406.41003 [4] Fyfe I. J.: Linear dependence relations connecting equal interval N-th degree splines and their derivatives. J. Inst. Maths. Appl. 7 (1971), 398-406. · Zbl 0219.65010 · doi:10.1093/imamat/7.3.398 [5] Hoskins W. D., Meek D. S.: Linear dependence relations for polynomial splines at midknots. BIT 15 (1975), 272-276. · Zbl 0311.65002 · doi:10.1007/BF01933659 [6] Kobza J.: Spline functions. Nakl. UP, Olomouc, 1993, 224 pp.) · Zbl 0791.41015 [7] Kobza J.: Quadratic splines interpolating derivatives. Acta Univ. Palacki. Olomuc., Fac rer. nat. 100, Math. 30 (1991), 219-233. · Zbl 0758.41005 [8] Kobza J.: Quartic interpolatory splines. Proc. NMTP, Pilsen 1993, 89-96. [9] Kobza J.: Some algorithms for computing local parameters of quartic interpolatory splines. Acta Univ. Palacki. Olomuc., Fac. rer. nat. 114, Math. 33 (1994), 63-73. · Zbl 0851.41009 [10] Kobza J.: Interpolatory and smoothing splines of even degrees. Proc. ISNA ’92, P.III, Prague 1992, 122-136. [11] Spaeth H.: Spline-Algorithmen zur Konstruktion glatter Kurven und Flaechen. Oldenbourgh Verlag, 1973, 134 pp. · Zbl 0276.65006 [12] Spaeth H.: Eindimensionale Spline-Interpolations-Algorithmen. Oldenbourgh Verlag, 1990, 390 pp. · Zbl 0701.41015 [13] Zavjalov J. S., Kvasov B. I., Miroschnichenko V. L.: Methods of Spline-Functions. Moscow, 1980 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.