A closed algebraic interpolation curve

We introduce a new interpolation method employing a closed algebraic curve. This note describes a trigonometric interpolation method to connect a give n point sequence in R-d by an algebraic and therefore smooth closed curve. The interpolation formula is of Lagrangian type and seems to be new. In con trast to spline interpolation our method does not work piecewise but global . Nevertheless the curve connects the given points in a quite natural manne r preserving the given order and without overshooting tendency. The curves are, like spline curves, stable in the following sense: changing the positi on of a single point of the given sequence only changes the curve in the ne ighbourhood of this point essentially. Besides its trigonometric parametriz ation the curve possesses a numerically efficient parametrization on the ba sis of Chebyshev polynomials of the second kind. To what extend the new int erpolation method can replace the spline method, the experts may decide. (C ) 2000 Elsevier Science B.V. All rights reserved.