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Smooth Matrix Interpolation

From: robert Macy
Subject: Smooth Matrix Interpolation
Date: Tue, 04 Nov 2003 14:24:48 -0800

Need some help, please.  Need a mathematical manipulation
to smooth a coarse matrix. 

Two choices:

1. Curve fit with better than 0.2% accuracy
2. Interpolate very finely.  

Basically, the matrix is 13 by 13  Each data point takes
over 20 hours to generate, so hate to fill in with "actual"

The shape of the surface is weird, with a major "dent" in
it.  My first attempt at curve fit was only good to 0.5%
over a restricted region.  

Linear interpolation made crawling around the matrix smooth
enough, but a subsequent differential operation caused a
"sawtooth" to form in the output which then starts
dominating the output.  Unacceptable.  

Anyone know how to fill in my matrix?  Or do an arbitrary
curve fit?  Problem with most curve fitting is that the
results simply get near the data points, yet I know the
data points are actual and should be intercepted exactly. 

The values around the center near  matrix(7,7) need to
preserve their accuracy while the accruacy at the edges and
corners is not so necessary like at matrix(1,1) or matrix
(1,13) or matrix (13,1) or matrix (13,13)  Even the edges
can be sacrificed, like at matrix(1,7) etc   

Maximum matrix element to minimum matrix element is around
60 to 1 

Any programs to help me?  

                  - Robert -

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