[geeks] Math Question

[Joshua D Boyd]

On Thu, Apr 11, 2002 at 07:56:30AM -0400, Michael A. Turner wrote:

<snip>

> "One way of determining the largest eigenvalue for a particular matrix is to
> use the Power Method (described in section 3.3 Schilling & Harris). StudyP
> 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...
> 
> 	Answer mw back off list or on, I don't care but for the love of god
> if you know what the closed form is tell me! Or better yet point me to a
> resource so I can learn about it.

Err, wouldn't complexity usually be expressed in terms of O(n^2) rather than
NxN?

Anyway, for the life of me I can't remember closed form w.r.t. eigenvalues.
But, some search indicates that it means something along the lines of
the formula for the solution.  For instance some places talk in terms of
closed form and/or numerical form (i.e. the number) of a problem.  This
definition appears to hold consistent with the usage of closed form in various
academic papers.  For instance, one college site states that most differential
equations don't have a closed form, and to my understanding it is true that
most differential equations only have numerical solutions.

Can't you find that term anywhere in your l.a. text?

Hope this helps a little.  Wish I could offer something more definitive.

-- 
Joshua D. Boyd