[R] interpolation and extremum location of a surface‏

[Hans W Borchers]

Clement LAUZIN <lauzin <at> hotmail.com> writes:

> Hello,
> 
> Hello,
> 
> I have a x,y,z file.Z is not corresponding to a simple analytical function
> of x and y (see below). I am trying to find the minimum location of this
> surface and the z value corresponding to this location by a spline
> interpolation or from a polynomial fit. I tried with the akima package but
> as the location of the point I am looking for (the minimum) is outside of
> the convex hull it's not giving any answer.
> If someone has any idea or any suggestion?
> 
> Thank you in advance Pierre 

According to a 2-dimensional barycentric Lagrange interpolation that
I am implementing right now in R, the minimum appears to be at

    x0 = (4.230490, 68.52776); fval = -175.7959

I certainly would be interested to hear from other reasonable locations
of a minimum, as this may be a good test case.

--  Hans Werner

> x    y    z
> 4.1 60 -152.1719593
> [ ... ]
> 4.35 90 -163.8389615
>