Rational Trigonometric Interpolation and Constrained Control of the Interpolant Curves

Abstract

In the present paper a new method is developed for smooth rational cubic trigonometric interpolation based on values of function which is being interpolated. This rational cubic trigonometric spline is used to constrain the shape of the interpolant such as to force it to be in the given region by selecting suitable parameters. The more important achievement mathematically of this method is that the uniqueness of the interpolating function for the given data would be replaced by uniqueness of the interpolating curve for the given data and selected parameters. Approximation properties have been discussed and confirms that the expected approximation order is ) (

On Trigonometric Numerical Integrator for Solving First Order Ordinary Differential Equation

“…The order of approximation of the developed interpolating function was found to ( ) 3 0 h . [8] developed a new method for smooth rational cubic trigonometric interpolation based on values of function which is being interpolated. This rational cubic trigonometric spline is used to constrain the shape of the interpolant in such a way that the uniqueness of the interpolating function for the given data would be replaced by uniqueness of the interpolating curve for the given data.…”