Shape-preserving piecewise rational interpolant with quartic numerator and quadratic denominator
An explicit representation of a piecewise rational interpolant with quartic numerator and quadratic denominator is presented. For positivity data, monotone data and convex data, the shape-preserving properties of the interpolant are given. The interpolant is C 2 continuous spline with a shape parameter w i on each subinterval. The values of w i to guarantee shape preservation are estimated. A convergence analysis establishes an error bound in terms of w i and shows that the interpolant is O ( h 2 ) or O ( h 3 ) accurate. Several examples are supplied to support the practical value of the given interpolation method.