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Stochastic gradient

  1. May 14, 2007 #1

    I have a random grid, meaning that each cell consists of a random number. I need to evaluate the gradient.

    I've tried to apply a basic Euler formula (u_(i+1) - u_(i-1))/2dx but since the values can fluctuate a lot, fluctuations are even stronger for the gradient...
    I'm thinking about using a "smoother" method like a five point stencil, which could be better to avoid strong fluctuations... but then I can't find out how to deal with grid boundaries (for Euler method I use (u_(i+1)-u(i))/dx or (u_(i)-u_(i-1))/dx )

    How would you do, is there a specific method for this kind of problem ?

    Thanks a lot
  2. jcsd
  3. May 15, 2007 #2
    how about [tex]u_{-1}:=2u_{0}-u_{1}[/tex], etc? I mean (linear) extrapolation.
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