Fast way in Matlab to compute inverse of big matrix 10800x10800?

Question

I have a matrix of size 10800x10800 in Matlab and I compute its inverse directly with the function:

inv(A)

It takes 3 to 4 minutes just one such computation. And that is part of an iterative algorithm which needs more than 20 iterations, so overall things would be very slow. Is there a better way to do this? Maybe some mathematical formulas or maybe a better Matlab function?

Edit: The matrix is diagonal. Each iteration the diagonal elements are updated based on formulas for fitting a factor analyzer. But that is irrelevant, the important thing is that it is a diagonal matrix and it changes each iteration.

THanks

Answer 1

If your matrix is indeed diagonal, you can obviously just do

Ainv = diag(1./diag(A));

which should be very fast.

Answer 2

The backslash operator \ is said to be faster and also could be more accurate. Without MATLAB really I cannot tell, but you could try to run A \ eye(10800) instead of inv(A), and see if it works out.