Dear forum members,(adsbygoogle = window.adsbygoogle || []).push({});

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,

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# Stochastic approximation applied to fixed source problem

Can you offer guidance or do you also need help?

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