Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

How does Mathematica interpolate in higher dimensions ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97712] How does Mathematica interpolate in higher dimensions ?
  • From: ben.whitehouse at gmail.com
  • Date: Thu, 19 Mar 2009 02:12:31 -0500 (EST)

Hi,

I have tri-variate histograms, which count the number of points from a
large group of (x,y,z)'s that fall within a 3D grid.

I then use

func = Interpolation[histogram, InterpolationOrder->1]

to create a linear Interpolation over the histogram's grid for the
various "heights" of the grid.

My question, though, is what is mathematica doing to make this
interpolation?

My best guess is that it is solving
f = a1 +a2 x + a3 y + a4 z + a5 x y + a6 x z + a7 y z + a8 x y z

using the 8 corner points of each cube.

It is not clear to me how this generalizes to higher orders, but I am
only interested in the linear case anyway.

Is the method documented anywhere ? or does anyone know ?

Thanks
Ben


  • Prev by Date: Internet connectivity -- CountryData
  • Next by Date: demonstrations and presentations
  • Previous by thread: Re: Internet connectivity -- CountryData
  • Next by thread: Re: How does Mathematica interpolate in higher dimensions ?