Positivity Preserving Interpolation of Positive Data by Cubic Trigonometric Spline

Abstract

For smooth and visualizing pleasant curve, we construct a positivity preserving interpolation by using alternative spline that is, cubic trigonometric spline with two shape parameters. In the description of the cubic trigonometric spline interpolant, positivity is preserved everywhere and has a unique representation for the positivity. We develop a constraints on the shape parameters to preserve the shape of the positive data in the view of smooth and pleasant positive curve by trigonometric interpolant. The degree of smoothness of the under discussion scheme is $C^1.$ Keywords: Cubic Trigonometric Spline; Shape Preservation; Interpolation; Positivity; Positive Data; Shape parameters. 2010 Mathematics Subject Classification 65D05, 65D07, 65D17, 65D18, 65U07.