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multivariate interpolation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110911] multivariate interpolation
  • From: Silvio Abruzzo <silvio.abruzzo at gmail.com>
  • Date: Sun, 11 Jul 2010 06:19:35 -0400 (EDT)

Dear Group,
  I have the following problem. I have a matrix of this form
{{{9, 0.01, 1001, 269250000,
   0.944218 - 12.6734 Sqrt[1/x] + 72.8455/x}, {10, 0.01, 1001,
   269250000, 0.944134 - 13.1619 Sqrt[1/x] + 71.1457/x}, {11, 0.01,
   1001, 269250000, 0.944054 - 13.6278 Sqrt[1/x] + 69.5111/x},....

where the first two numbers are parameters and the third and fourth
number represent the bounds where the function in the last entries is
usable. I would like to interpolate the first, second and last column
in such a way that I have as result a function f[a_, b_, x_] were when
a and b are fixed and corresponds to some value in the matrix above
the function in the last column is used and when there is not the
corresponding entry the interpolation is used. A method to achieve my
goal is to calculate in some point between the min and the max the
function in the last column in order that I have a tensor product
structure and then to use the function Interpolation. Although this
method should work enough well, I would like to know if there is a
method to use all analytical information contained in the function in
the last column in order to produce a better interpolation.


Best regards,

Silvio


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