A fractal procedure for monotonicity preserving interpolation

- Interpolation subject to strip condition on first derivative is considered with a FIF.
- Shape parameters involved in the FIF controls shape of the curve near left and right end points.
- Some traditional rational splines emerge as special cases of the FIF.
- Derivative of the monotonic rational FIF may be nondifferentiable in a finite or dense subset of interval.

This paper is concerned with interpolation subject to a strip condition on the first order derivative using a class of rational cubic Fractal Interpolation Functions (FIFs). This facilitates the FIF to generate monotonic curves for a given set of monotonic data. The proposed monotonicity preserving rational FIF subsumes and supplements a classical monotonic rational cubic spline. In models leading to the monotonicity preserving interpolation problem wherein the first order derivative of the constructed interpolant is to be nondifferentiable in a finite or dense subset of the interpolation interval, the developed fractal scheme is well-suited in contrast to its classical nonrecursive counterpart. It is shown that the present fractal interpolation scheme has O(h4) accuracy, provided the original function belongs to C4(I) and the parameters involved in the FIF are appropriately chosen.