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Stochastic approximation applied to fixed source problem

  1. Apr 18, 2013 #1
    Dear forum members,


    I am trying to solve the following system of equations.

    ψ(x,y,z)=∫∫ψ(x',y',z)K(x',y',z)dx'dy'

    z=f(ψ)

    What I do is to solve the integral equation with a Monte Carlo method, evaluate "z" and do a loop until convergence.

    My question to you is whether it is possible to accelerate the convergence by using stochastic approximation method such as Stochastic gradient descent (a.k.a. Robbins-Monro). I would highly appreciate any comments on the subject, including general information about the Robbins-Monro algorithm. What I know about the Robbins-Monro algorithm is that it is used to find zeros of nonlinear stochastic equations. Can It be applied to stochastic Fredholm problems like the one above?


    Thank you in advance,
     
  2. jcsd
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