Summary
The projectional properties and associated global and local error bounds for quadratic interpolatory splines are studied, along with applications to the numerical solution of two-point boundary value problems via collocation.
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References
Birkhoff, G., de Boork, C.: Error bounds for spline interpolation. J. Math. Mech.13, 827–835 (1964)
de Boor, C., Fix, G. J.: Spline approximation by quasi-interpolants. J. Approx. Theory8, 19–45 (1973)
de Boor, C., Swartz, B. K.: Collocation at Gaussian points. SIAM J. Numer. Anal.10, 582–606 (1973)
Cheney, E. W., Schurer, F.: Convergence of cubic spline interpolants. J. Approx. Theory3, 114–116 (1970)
Hall, C. A.: Uniform convergence of cubic spline interpolants. J. Approx. Theory7, 71–75 (1973)
Kammerer, W. J., Reddien, G. W.: Local convergence of smooth cubic spline interpolation. SIAM J. Numer. Anal.9, 687–694 (1972)
Kershaw, D.: Inequalites on the elements of the inverse of a certain tri-diagonal matrix. Math. Comp.24, 155–158 (1970)
Lorentz, G. G.: Approximation of functions. New York: Holt, Rinehart, and Winston 1966
Lucas, T. R.: Error bounds for interpolating cubic splines under various end conditions. SIAM J. Numer. Anal. (to appear)
Lucas, T. R., Reddien, G. W.: Some collocation methods for nonlinear boundary value problems. SIAM J. Numer. Anal.9, 341–356 (1972)
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
Marsden, M. J.: Cubic spline interpolation of continuous functions. J. Approx. Thoery10, 103–111 (1974)
Marsden. M. J.: Quadratic spline interpolation, to appear in Bull. Amer. Math. Soc.
Meir, A., Sharma, A.: On uniform approximation by cubic splines. J. Approx. Theory2, 270–274 (1969)
Nord, S.: Approximation properties of the spline fit. BIT7, 132–144 (1967)
Swartz, B. K., Varga, S.: Error bounds for spline and L-spline interpolation. J. Approx. Theory6, 6–49 (1972)
Varga, R. S.: Matrix iterative analysis. Englewood Cliffs, New York: Prentice-Hall 1962
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
de Boor, C.: On bounding spline interpolation. J. Approximation Theory (to appear)
Swartz, B.: ϕ (h 2n+2−1) bounds on some spline interpolation errors. Bull. Amer. Math. Soc.74, 1072–1078 (1968)
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Research supproted in part by the U.S. Atomic Energy Commission under Grant AT (11-1)-2075.
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Kammerer, W.J., Reddien, G.W. & Varga, R.S. Quandratic interpolatory splines. Numer. Math. 22, 241–259 (1974). https://doi.org/10.1007/BF01406966
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DOI: https://doi.org/10.1007/BF01406966