[geeks] Math Question

[Michael A. Turner]

	If I still had the L.A. text I would be good, but this is the next
class along and the selling of that book helped finance getting this book...
This is for my computational methods class. I found a WHOLE bunch of sites
that use this method, but unfortunately they are all seem to be master and
doctoral thesis papers and are a little short on describing how they got to
their answers. They are assuming that anyone reading the paper would already
know. 
	He does not state that he wants this complexity based on big O
theory, I may convert it to that before I submit it, as it seems to be the
right form. He has never brought it up before but a pre-requisite class did
cover that. 

Michael A. Turner
Systems Engineer
WHRO
michael.turner at whro.org
http://www.whro.org


-----Original Message-----
From: Joshua D Boyd [mailto:jdboyd at cs.millersville.edu]
Sent: Thursday, April 11, 2002 8:59 AM
To: geeks at sunhelp.org
Subject: Re: [geeks] Math Question


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