Dear N.R.s:

I have encountered a perplexing complication when attempting
to apply cubic spline interpolation to certain sets of
tabulated data. Specifically, if the values of the data
exhibit steep ascents, descents, or oscillations, the
CSI interpolated values often exhibit wild excursions
above or below the bracketing tabulated values. In other
words, they bulge!

I encoutered this in the context of tabulated values of
thermonuclear reaction rates as a function of temperature.
These rates are often comprised of a sum of exponentials
each multiplied by a gentle modulating function of temperature. One cannot just extract the exponential
causing the bulges and then CSI the gently varying
function.

One solution is to not use CSI at all, and instead use some type of monotonicity preserving Hermite interpolation, e.g.
Spath Interpolation. Continuous first derivatives are also
provided, but second derivatives are not.

Another solution could be to use CSI under tension, where the bulges are pulled away until monotonicity is recovered.

Is there such a thing as monotonicity preserving CSI under
tension?

It appears that everyone I know automatically uses CSI with
complete success. The very first time I ever used CSI
it was a disaster. Is my case exceptional?

Any comment or advice on this issue of CSI breakdown
will be welcome.

Sincerely,

tasande