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Quadratic splines smoothing the first derivatives. (English) Zbl 0757.65006

The author studies the problem of computing the quadratic spline with knots at \(a=x_ 0<x_ 1<\dots < x_ n<x_{n+1}=b\) which minimizes the expression \(\alpha\int^ b_ a[f''(x)]^ 2dx+\sum^{n+1}_{i=0}w_ i[f'(x_ i)-m_ i]^ 2\) for given values \(\{m_ i\}_ 0^{n+1}\), parameter \(\alpha\) and weights \(w_ i\geq 0\), \(i=0,\dots,n+1\).

MSC:

65D07 Numerical computation using splines
65D05 Numerical interpolation
65D10 Numerical smoothing, curve fitting
41A15 Spline approximation
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References:

[1] Ahlberg J. H., Nilson E. N., Walsh J. L.: The Theory of Splines and Their Aplications. Academic Press, N.Y., 1967. · Zbl 0158.15901
[2] de Boor C.: A Practical Guide to Splines. Springer Verlag, N.Y., 1978. · Zbl 0406.41003
[3] Kobza J.: An algorithm for parabolic splines. Acta UPO, FRN 88 (1987), 169-185. · Zbl 0693.65005
[4] Kobza J.: Quadratic splines interpolating the first derivatives. Acta UPO, FRN 100 (1991), 219-233. · Zbl 0758.41005
[5] Kobza J., Zápalka D.: Natural and smoothing quadratic spline. Applications of Mathematics 36 no. 3 (1991), 187-204. · Zbl 0731.65006
[6] Laurent P.-J.: Approximation et Optimization. Hermann, Paris, 1972.
[7] Sallam S., Tarazi M.N.: Quadratic spline interpolation on uniform meshes. In Splines in Numerical Analysis (Schmidt J.W., Spaeth H., Akademie-Verlag, Berlin, 1989, pp. 145-150. · Zbl 0677.65010
[8] Schultz M.: Spline Analysis. Prentice-Hall, Englewood Cliffs, N.Y., 1973. · Zbl 0333.41009
[9] Vasilenko V.A.: Spline Functions: Theory, Algorithms, Programs. Nauka, SO, Novosibirsk, 1983. · Zbl 0529.41013
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