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MathGroup Archive 2007

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Re: Re: Intensive numerical calculations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80465] Re: [mg80416] Re: Intensive numerical calculations
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Thu, 23 Aug 2007 01:04:27 -0400 (EDT)
  • References: <f9s445$all$1@smc.vnet.net><fabgog$id8$1@smc.vnet.net> <fae9u4$ec7$1@smc.vnet.net> <200708220838.EAA08507@smc.vnet.net>

Cristian wrote:
> On Tue, 21 Aug 2007 09:06:12 +0000 (UTC), Yaroslav Bulatov
> <yaroslavvb at gmail.com> wrote:
> 
> 
>>Efficiency can vary depending on your implementation. For instance
>>here's a range of solutions to the problem of sampling markov chains,
>>and their execution times varies by a factor of more than 2000. The
>>fastest solution had similar runtime to optimized C code.
>>
>>http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/21f088453d0c6745/5e9853ea4489135d?lnk=st&q=&rnum=1#5e9853ea4489135d
>>
> 
> 
> They are academic examples or almost..... tries to work with matrixes
> of 10^5 x 10 ^5 ( double)  and to use some graphics and to hold
> everything in memory... he goes to footstep of snail and there is no
> solution... Real problem (structural project for examples )...We can
> climb only on the mirrors...(matlink, etc etc etc..)  And then test in
> c++ ...compile and  use.....
> thanks
> cristian

What are you doing with these matrices? Finding a few of the largest 
eigenvalues? Are you using a sparse representation?

With a dense representation your matrix will occcupy around 10^11 bytes, 
far more than Mathematica can handle. Possibly at some time in future 
the 64-bit version will allow for such memory usage.

Suffice it to say that a dense representation will cause problems for 
most software on many machines. As for a sparse represntation, and 
computational speed, it will depend on what specifically you want to do. 
Mathematica uses some fairly good libraries for certain linear algebra 
operations on such matrices. If what you require is not well supported 
then you might need to go to some other approach, perhaps via MathLink.

Daniel Lichtblau
Wolfram Research





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