[geeks] Math Question

[S. Gwizdak]

> "One way of determining the largest eigenvalue for a particular matrix is to
> use the Power Method (described in section 3.3 Schilling & Harris). Study
> the implementation of the power method as described in alg. 3.3.1 (pg. 107).
> Express in closed form the mathematical complexity for a single iteration of
> the method for any matrix of size n x n (assume all multiply/adds are the
> same in cost). " 
> 
> 	I think I have the answer to this, the method does one matrix
> multiplication per iteration making it NxN complexity where n is of course
> the matrix sizes. I just am unsure of what closed form is. I have a
> suspicion that my linear algebra teacher forgot a section in that class and
> now my knowledge is swinging in the breeze here...

Watch out.

It could be NxNxN.

Matrix multiplication is O(N^3) in the simple way of doing it. (You have
to add all the numbers after all the multiplications, bringing in the 
extra factor of N.) I'm not sure what this question is asking for since
it's been a few years since I've had linear algebra. (Note the last line
of the question.)