×

zbMATH — the first resource for mathematics

Quadratic interpolatory splines. (English) Zbl 0271.65006

MSC:
65D05 Numerical interpolation
65L10 Numerical solution of boundary value problems involving ordinary differential equations
41A15 Spline approximation
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Birkhoff, G., de Boork, C.: Error bounds for spline interpolation. J. Math. Mech.13, 827-835 (1964) · Zbl 0143.28503
[2] de Boor, C., Fix, G. J.: Spline approximation by quasi-interpolants. J. Approx. Theory8, 19-45 (1973) · Zbl 0279.41008 · doi:10.1016/0021-9045(73)90029-4
[3] de Boor, C., Swartz, B. K.: Collocation at Gaussian points. SIAM J. Numer. Anal.10, 582-606 (1973) · Zbl 0232.65065 · doi:10.1137/0710052
[4] Cheney, E. W., Schurer, F.: Convergence of cubic spline interpolants. J. Approx. Theory3, 114-116 (1970) · Zbl 0193.02503 · doi:10.1016/0021-9045(70)90065-1
[5] Hall, C. A.: Uniform convergence of cubic spline interpolants. J. Approx. Theory7, 71-75 (1973) · Zbl 0247.41008 · doi:10.1016/0021-9045(73)90054-3
[6] Kammerer, W. J., Reddien, G. W.: Local convergence of smooth cubic spline interpolation. SIAM J. Numer. Anal.9, 687-694 (1972) · Zbl 0251.65003 · doi:10.1137/0709057
[7] Kershaw, D.: Inequalites on the elements of the inverse of a certain tri-diagonal matrix. Math. Comp.24, 155-158 (1970) · Zbl 0229.15012 · doi:10.1090/S0025-5718-1970-0258260-5
[8] Lorentz, G. G.: Approximation of functions. New York: Holt, Rinehart, and Winston 1966 · Zbl 0153.38901
[9] Lucas, T. R.: Error bounds for interpolating cubic splines under various end conditions. SIAM J. Numer. Anal. (to appear) · Zbl 0255.65008
[10] Lucas, T. R., Reddien, G. W.: Some collocation methods for nonlinear boundary value problems. SIAM J. Numer. Anal.9, 341-356 (1972) · Zbl 0266.34024 · doi:10.1137/0709034
[11] Lyche, T., Schumaker, L. L.: On the convergence of cubic interpolating splines. In: Spline functions and approximation theory (A. Meir and A. Sharma, ed.), pp. 169-189, Basel: Birkhäuser 1973 · Zbl 0255.41009
[12] Marsden, M. J.: Cubic spline interpolation of continuous functions. J. Approx. Thoery10, 103-111 (1974) · Zbl 0281.41002 · doi:10.1016/0021-9045(74)90109-9
[13] Marsden. M. J.: Quadratic spline interpolation, to appear in Bull. Amer. Math. Soc.
[14] Meir, A., Sharma, A.: On uniform approximation by cubic splines. J. Approx. Theory2, 270-274 (1969) · Zbl 0183.33002 · doi:10.1016/0021-9045(69)90023-9
[15] Nord, S.: Approximation properties of the spline fit. BIT7, 132-144 (1967) · Zbl 0171.37304 · doi:10.1007/BF01934276
[16] Swartz, B. K., Varga, S.: Error bounds for spline and L-spline interpolation. J. Approx. Theory6, 6-49 (1972) · Zbl 0242.41008 · doi:10.1016/0021-9045(72)90079-2
[17] Varga, R. S.: Matrix iterative analysis. Englewood Cliffs, New York: Prentice-Hall 1962 · Zbl 0133.08602
[18] Brikhoff, G., de Boor, C.: Piecewise polynomial interpolation and approximation. In: Approximation of functions (H. L. Garbedian, ed.), pp. 164-190. New York: Elsevier Publishing Co. 1965
[19] de Boor, C.: On bounding spline interpolation. J. Approximation Theory (to appear) · Zbl 0302.41006
[20] Swartz, B.: ? (h 2n+2-1) bounds on some spline interpolation errors. Bull. Amer. Math. Soc.74, 1072-1078 (1968) · Zbl 0181.34001 · doi:10.1090/S0002-9904-1968-12052-X
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.