Matrix power vs for loop

Question

L 2023-6-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1988428-matrix-power-vs-for-loop

回答： James Tursa 2023-6-26

Hi.

I have to iterate a linear system of the type x(k+1) = Ax(k), with x being a vector of 1024 elements. I only care about the last vector obtained, this is, x(endtime).

What would be faster?

x0 =rand(1024,1)
x = x0;
for i = 1:endtime
    x = A*x 
end

or

x = (A^endtime) * x0

Thanks.

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Answer 1

Angelo Yeo 2023-6-26

1
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https://ww2.mathworks.cn/matlabcentral/answers/1988428-matrix-power-vs-for-loop#answer_1262883

在 MATLAB Online 中打开

Hi Luisa,

If you only want to calculate the time it took to run a snippet of code, you can use tic and toc. Below is an example. You can see the latter one is faster.

endtime = 10000;
A = rand(1024, 1024);
case1 = tic;
x0 =rand(1024,1);
x = x0;
for i = 1:endtime
    x = A*x;
end
toc(case1)
Elapsed time is 1.614399 seconds.
case2 = tic;
x = (A^endtime) * x0;
toc(case2)
Elapsed time is 0.245417 seconds.