Find square root using Monte carlo?

27 次查看（过去 30 天）
RSR
RSR 2015-5-19
评论： Walter Roberson 2023-4-11
derive numerical value of square root of 2 using MC
  2 个评论
James Tursa
James Tursa 2015-5-19
Were you given any more instructions in the assignment? What have you done so far?
John D'Errico
John D'Errico 2015-5-19
编辑：James Tursa 2015-5-19
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.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

Brandon
Brandon 2015-5-19
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 2015-5-19
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 个评论
Atishay Jain
Atishay Jain 2018-2-21
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 2023-4-11
Ran in:
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

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Code Performance 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by