Re: RBF Interpolation
- From: highegg <highegg@xxxxxxxxx>
- Date: Fri, 10 Apr 2009 01:27:59 -0700 (PDT)
On Apr 10, 7:10 am, Bo Schwarzstein <Bo.Schwarzst...@xxxxxxxxx> wrote:
Hello everyone,
Is there anybody worked on RBF interpolate the scattering data point
cloud ? Why I could get some negative weights ? I use the gaussian
function \phi = exp(-r*c*c), I found if I modify the "c" from 0.00001
to 20000, sometimes the weights are all positive, that's very strange
to me.
Thansk !
A simple least squares RBF interpolation (which you probably refer to)
does not restruct weights to be positive, they will be negative if
that results in a lower residual. You can restrict the weights to be
positive, but then expect a higher residual (which may still be a
better fit from the practical sense). Using an excessively large c
shrinks the support of the gaussian to essentially a single point,
thus the weights will be almost surely positive if the centers are a
subset of the data, but the interpolant will probably be of no use.
.
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