Abstract
Abstract In this paper, trigonometric splines are used for Hermite interpolation of the data consist of functional values and their derivatives. If the derivative data is given, then we reparameterize the data suitably. Otherwise, we find them using a necessary and sufficient condition. We show that our Hermite interpolant preserves the monotonicity. We introduce the notion of H-convex and show that convexity of H-convex data is preserved by our Hermite interpolant. The biggest advantage of our method is that it reproduces ellipse. We also provide some numerical examples to validate our theory.KeywordsHermite interpolationQuadratic trigonometric splineShape preservationEllipse
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