The orders of approximation of the first derivative of cubic splines at the knots

Author:
D. Kershaw

Journal:
Math. Comp. **26** (1972), 191-198

MSC:
Primary 65D10

DOI:
https://doi.org/10.1090/S0025-5718-1972-0300403-0

MathSciNet review:
0300403

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Abstract: The order of approximation of the first derivative of four types of interpolating cubic splines are found. The splines are defined by a variety of endpoint conditions and include the natural cubic spline and the periodic cubic spline. It is found that for two types there is an increase in the order of approximation when equal intervals are used, and that for a special distribution of knots the same order can be realized for the natural spline.

**[1]**T. N. E. Greville, ``Spline functions, interpolation, and numerical quadrature,'' in*Mathematical Methods for Digital Computers.*Vol. 2, A. Ralston and H. S. Wilf (Editors), Wiley, New York, 1967. MR**35**#2516. MR**0223801 (36:6848)****[2]**D. Kershaw, ``The explicit inverses of two commonly occurring matrices,''*Math. Comp.*, v. 23, 1969, pp. 189-191. MR**38**#6754. MR**0238478 (38:6754)****[3]**D. Kershaw, ``Inequalities on the elements of the inverse of a certain tridiagonal matrix,''*Math. Comp.*, v. 24, 1970, 155-158. MR**41**#2907. MR**0258260 (41:2907)****[4]**D. Kershaw, ``A note on the convergence of interpolatory cubic splines,''*SI AM J. Numer. Anal.*, v. 8, 1971, pp. 67-74. MR**0281318 (43:7036)**

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DOI:
https://doi.org/10.1090/S0025-5718-1972-0300403-0

Keywords:
Interpolation,
cubic splines

Article copyright:
© Copyright 1972
American Mathematical Society