vectorized fzero function for Monte Carlo simulation

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wangm 2021-10-6

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回答： wangm 2021-10-8

I am run a Monte Carlo simulation with e.g. 1 million realizations and there is a zero searching using the fzero function in each loop. The code becomes very slow for 1 million loops. Is there a vectorized way for fzero? The code likes:

for i = 1:1e6

x(i) = fzero(fun, x0)

end

Is there a quick way like: x = vectorized_fzero(fun, x0) to improve the efficiency?

Thanks

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Answer 1

Walter Roberson 2021-10-6

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No.

However if you happen to know the derivative of the function or can construct it symbolically, then you can create a vectorized version of the Newton Raphson method.

Selection of which entries to process further can end up being more expensive than just processing all of the entries in some cases, depending on how expensive the function is.

The number of digits gain per iteration is known in theory so you can often put in a fixed upper limit on the number of iterations.

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Answer 2

wangm 2021-10-8

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not familar with your solution. does it work with multiple random variabes? the x in equation is a vector of x1, x2,... and x1, x2,... are sampled from their respective distribution. I just wonder if someone has made fzero applicable to this situation.