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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: interpolating/smoothing w/ monotonically increasing
Date: Thu, 30 Oct 2008 20:58:01 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Pete sherer" <tsh@abg.com> wrote in message <ged2vl$ep1$1@fred.mathworks.com>...
> Thanks Bruno.  I would prefer some kinds of interpolation in stead of doing regression which might not fit well at the end point (like left point).  Is it doable?

No, it is not doable, but it depends upon exactly
what you mean by "doable". How will you choose
to interpolate non-monotonic data so that the
result is monotone?

Interpolation means that you will reproduce the
data points exactly. So if your data is not monotone
then an interpolant cannot possibly be monotonic.

The best you can do is something like what pchip
does. Pchip will not introduce new local extrema
into the curve where the curve was monotone.
It will be as monotone as is the data.

Or, you can do as I did in my last post, where I
showed how to use a constrained least squares
to find the minimal change to your data points
such that the result is monotone.

These are the only two alternatives I'd suggest
There are of course others, subtle variations on
the above themes, but not much different.

John