How can I achieve a spline interpolation such that when given non-decreasing sequence of points the resulting spline will also be a non-decreasing function (and vice-versa, when given non-increasing sequence the interpolation would also be non-increasing)?
For example, here is a natural cubic spline interpolation: http://i.stack.imgur.com/W5yPA.png
over the following dataset:
270 71 333 102 355 109 406 111 427 168As you can see, the polynom between points [355, 109] and [406, 111] is decreasing at some interval.
What kind of spline is best suited for such "monotone" interpolation?
EDIT: so here is the result of monotone cubic Hermite interpolation using Fritsch–Carlson method suggested by bubba: