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Find square root using Monte carlo?

23 Ansichten (letzte 30 Tage)
RSR
RSR am 19 Mai 2015
Kommentiert: Walter Roberson am 11 Apr. 2023
derive numerical value of square root of 2 using MC
  2 Kommentare
James Tursa
James Tursa am 19 Mai 2015
Were you given any more instructions in the assignment? What have you done so far?
John D'Errico
John D'Errico am 19 Mai 2015
Bearbeitet: James Tursa am 19 Mai 2015
Easy peasy. For example, to find the square root of 2...
X = 2;
Xroot = 1;
while Xroot.^2 ~= X
Xroot = X*rand;
end
When it converges, you are done. Of course, that may take some serious time. Just thinking, but I'm wondering just how many completely unworkable (but in theory, valid) answers I can think of for this problem? I'll bet I can think of at least a few more.
If you want a better answer, you will need to make more effort than simply posting your assignment.

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Antworten (2)

Brandon
Brandon am 19 Mai 2015
This sounds like a homework assignment, so nobody here is going to answer it directly for you.
This website might give you some inspiration though: http://mathfaculty.fullerton.edu/mathews/n2003/montecarlopimod.html
In this problem, pi is the unknown value. Let's say you knew pi, would you be able to find another parameter? The answer is yes. Now how do you make that parameter equal to sqrt(2)...?

Walter Roberson
Walter Roberson am 19 Mai 2015
Generate a random value between 0 and 2. Square it. If the square is <= 2 then add 1 to a counter. Repeat this fixed number of times. The ratio between the counter and the number of times you repeated this will approach sqrt(2)/2.
  2 Kommentare
Atishay Jain
Atishay Jain am 21 Feb. 2018
I can't figure out why it will approach sqrt(2)/2 ... It's not areas of square with side sqrt(2)/ area of square with side 2.
What is it?
Thank you!
Walter Roberson
Walter Roberson am 11 Apr. 2023
N = 100000;
approximation = mean((rand(1,N)*2).^2 <= 2)
approximation = 0.7081
square_root_2 = approximation * 2
square_root_2 = 1.4162
square_root_2 * square_root_2
ans = 2.0055

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