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Hi Walter,
as a guy who likes to use Markov processes a lot as a means of quantifying
trading decisions, I can certainly confirm that 300-row matrices can and do
occur in "every-day" calculations. Luckily for today's computer users,
today's computers are equal to the task.
To give a concrete numerical example of a larger-type matrix calculation, I
had Mathematica build a 300x300 matrix consisting of double-precision random
numbers between 0 and 1 (as would be typical for transition probabilities in
Markov chains). I thought it might be instructive to list the durations for
Mathematica to define the 300x300 matrix, then take its determinant and its
inverse - quite a task, actually, which not so long ago would have required
an expensive workstation computer to do the calculations in reasonable time.
Here are Mathematica's results on my old 450 MHz PIII, and, mind, running in
interpretive mode, i.e.. without compilation:
Fill 300x300 matrix with double-precision numbers: 0.1 sec
Take the determinant of that matrix: 0.4 sec
Invert 300x300 matrix: 1.7 sec
As we know from working with Hilbert matrices, it is good to be suspicious
of larger-scale iterative results; so I checked the results by doing the
same calculation with higher than double-precision accuracy which is 16
digits. I chose an internal precision of 50 decimal digits; the above
results had been OK, though, and times were just a little longer for the
high-accuracy calculations, with 0.5 sec and 1.8 sec, respectively.
I don't know if this is of any interest to you or the list, just thought I'd
add my two cents' worth.
Best,
Michael Suesserott
> -----Ursprüngliche Nachricht-----
> Von: owner-metastock@xxxxxxxxxxxxx
> [mailto:owner-metastock@xxxxxxxxxxxxx]Im Auftrag von W Lake
> Gesendet: Thursday, September 06, 2001 15:59
> An: metastock@xxxxxxxxxxxxx
> Betreff: Numerical Linear Algebra
>
>
> Hi Lionel
>
> As the introductory paragraph at the site says:
>
> "... software for the solution of linear algebra problems ..."
> "... for solving problems in numerical linear algebra, ..."
>
> trading is not mentioned
>
> Most college books on linear algebra usually deal with small
> matrices, i.e.,
> 3 rows x 5 columns, whereas in business and in trading you are
> going to need
> at least 300 rows x "lots" of variables, etc. Problems of this size are
> referred to as numerical linear algebra.
>
> Michael can probably be of more help in describing the
> "difference" between
> the two. The terms used become complicated and merge with
> computer science,
> i.e., linear programming.
>
> Some of the programs listed at the site are for parallel
> processing or even
> for large supercomputers, i.e., Crays, but as you know, we
> average guys are
> dealing with more horsepower every year.
>
> Best regards
>
> Walter
>
> ----- Original Message -----
> From: Lionel Issen <lissen@xxxxxxxxxxxxxx>
> To: <metastock@xxxxxxxxxxxxx>
> Sent: Wednesday, September 05, 2001 8:37 PM
> Subject: Re: Numerical Linear Algebra
>
>
> > Can you tell me if the first site is oriented towards trading or is it a
> > strictly linear algebra site?
> > Lionel Issen
> > lissen@xxxxxxxxxxxxxx
> > ----- Original Message -----
> > From: "W Lake" <wlake@xxxxxxxxx>
> > To: <metastock@xxxxxxxxxxxxx>
> > Sent: Wednesday, September 05, 2001 11:59 PM
> > Subject: Numerical Linear Algebra
> >
> >
> > > Thanks
> > >
> > > was not aware of this site of available software. It sure makes
> searching
> > > easier <G>
> > > http://www.netlib.org/utk/people/JackDongarra/la-sw.html
> > >
> > > Trefethen and Bau's book looks very ineresting.
> > > http://www.siam.org/books/ot50/index.htm
> > >
> > > I guess someday you really have to graduate to the big matrices <G>
> > >
> > > Thanks again
> > >
> > > Walter
> > >
> > >
> >
> >
>
>
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