Endpoint formulas for interpolatory cubic splines

Seidman, Thomas I.; Korsan, Robert J.

doi:10.1090/S0025-5718-1972-0314228-3

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

Endpoint formulas for interpolatory cubic splines
HTML articles powered by AMS MathViewer

by Thomas I. Seidman and Robert J. Korsan PDF

Math. Comp. 26 (1972), 897-900 Request permission

Abstract:

In the absence of known endpoint derivatives, the usual procedure is to use a “natural” spline interpolant which Kershaw has shown to have $\mathcal {O}({h^4})$ error except near the endpoints. This note observes that either the use of appropriate finite-difference approximations for the endpoint derivatives or a proposed modification of the interpolation algorithm leads to $\mathcal {O}({h^4})$ error uniformly in the interval of approximation.

References

D. Kershaw, A note on the convergence of interpolatory cubic splines, SIAM J. Numer. Anal. 8 (1971), 67–74. MR 281318, DOI 10.1137/0708009