Matrix power vs for loop

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.

Answer 1

[Angelo Yeo]

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.

Answer 2

[James Tursa]

Note that the A^endtime method is probably going to be more accurate as endtime gets larger. The loop method can have a tendancy to build up errors.