hello,

My tabulated points are monotone increasing.
I wonder whether the natural cubic spline interpolant will also be monotone increasing throughout the range.

regards,

...I wonder ...

Try good ol' Wikipedia: Monotone cubic interpolation (http://en.wikipedia.org/wiki/Monotone_cubic_interpolation)

Regards,

Dave

To be slightly more informative, may I suggest looking into Steffen's interpolation or Fritsch-Carlson interpolation (called PCHIP in SLATEC and MATLAB), which are both based on piecewise Hermite cubics, or look into Stineman interpolation, which uses piecewise rational functions.

Jan M.