Abstract
The algorithm for solving interpolation problems with cubic splines is extended to fourth order generalized trigonometric splines. The attained tridiagonal linear system will be strictly diagonally dominant if the partition is sufficiently fine. If the function to be interpolated is in C2 then the order of the error between this interpolating generalized spline and the cubic spline will be 4. Hence the interpolation error is of fourth order when the given function is in C4. An upper bound for this error is found for a subclass of the generalized trigonometric splines.
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© 1984 D. Reidel Publishing Company
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Koch, P.E. (1984). Error Bounds for Interpolation by Fourth Order Trigonometric Splines. In: Singh, S.P., Burry, J.W.H., Watson, B. (eds) Approximation Theory and Spline Functions. NATO ASI Series, vol 136. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6466-2_21
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DOI: https://doi.org/10.1007/978-94-009-6466-2_21
Publisher Name: Springer, Dordrecht
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