Piecewise cubic monotone interpolation with assigned slopes (Q1179552)

The authors propose an algorithm to construct a monotonicity preserving cubic \(C^ 1\) interpolant, when the first derivatives also must be interpolated without modification. This method converges for functions of the class \(C^ 4\) with the order \(O(h^ p)\), where \(p\) is related to the order of approximation to the function on the knots.