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Volume :38 Issue : 1 2011      Add To Cart                                                                    Download

On semi-cardinal interpolation with cubic splines

Auther : AURELIAN BEJANCU

Department of Mathematics, Faculty of Science, Kuwait University, P.O. Box 5969 Safat 13060, Kuwait, Email: abejancu@yahoo.co.uk

ABSTRACT

We prove the existence and uniqueness of a cubic spline that interpolates data of power growth at the set of all non-negative integer knots, subject to one end condition. Our approach models a hierarchy of automatic end conditions in terms of finite differences for B-spline coefficients. We establish the order of convergence of the associated Lagrange schemes for semi-cardinal interpolation, the maximal order 4 being obtained for the `not-a-knot condition.

Keywords: Semi-cardinal interpolation; B-spline; approximation order; end conditions; not-a-knot.

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Jun 19, 2012

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