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what is computational complexity of matrix inversion algorithm in matlab?

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Shannon
Shannon 2011-7-28
what is computational complexity of matrix inversion algorithm in matlab? It's not listed in the help files as far as I can tell.

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the cyclist
the cyclist 2011-7-28
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).
the cyclist
the cyclist 2011-7-28
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().
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the cyclist
the cyclist 2011-7-28
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.

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Walter Roberson
Walter Roberson 2011-7-28
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.

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