what is computational complexity of matrix inversion algorithm in matlab?

what is computational complexity of matrix inversion algorithm in matlab? It's not listed in the help files as far as I can tell.

Answer 1

[the cyclist]

This page lists the computational complexity of three different matrix inversion algorithms:

http://en.wikipedia.org/wiki/Computational_complexity_of_mathematical_operations#Matrix_algebra

I have not yet found which of the three algorithms MATLAB uses for inv() [if, indeed, it uses any of them], but maybe this will help you get one step closer. Also, as Walter pointed out, MATLAB may use a different algorithm depending on the matrix size (or other properties).

Answer 2

[the cyclist]

Ordinarily, one can use the mlint() function, with the '-cyc' option, to measure the McCabe complexity. However, it seems to me that this will not work for built-in functions like inv().

[the cyclist]

FYI, my response assumed you were asking for the cyclomatic complexity (http://en.wikipedia.org/wiki/Cyclomatic_complexity) of the program. Seems to me now that you were actually asking about http://en.wikipedia.org/wiki/Computational_complexity_theory. Sorry for any confusion.

Answer 3

[Walter Roberson]

It may depend upon the properties of the matrix: specialized matrix forms may have different complexities. It could potentially also depend upon the condition number of the matrix, but I have no evidence of that.

An earlier Question about the computational complexity of eig and pinv went unanswered.