Parallel Gauss-Seidel with relaxation iterative algorithm...

[aminer10]

Hello,

Description:

The Parallel iterative with relaxation method that i programmed here is
designed to be used to solve large sparse systems of linear equations
where the direct methods can exceed available machine memory and/or
be extremely time-consuming. for example the direct method of the
Gauss algorithm takes O(n^2) in the forward elimination process and
is dominated by the O(n^3) back substitution process, that means, if
for example an operation takes 10^9 second and we have 1000 equations ,
the elimination process in the Gauss algorithm will takes 0.7 second, but
if we have 10000 equations in the system , the elimination process in the
Gauss algorithm will take 11 minutes !. This is why i have develloped for
you the Parallel Gauss-Seidel with relaxation iterative algorithm in Object Pascal,
that is very fast.

And please take a look at my article on my Parallel Gauss-Seidel
with relaxation algorithm:

http://pages.videotron.com/aminer/ParallelGaussSeidel/gsrp.htm

The benchmarks here:

http://pages.videotron.com/aminer/ParallelGaussSeidel/gsrp.htm.

Please look at my parallel program gsp.pas inside the zip file , compile and execute it ... -

You can download it from: http://pages.videotron.com/aminer/

Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/

Operating Systems: Win , Linux and Mac (x86).

Required FPC switches: -O3 -Sd -dFPC -dWin32 -dFreePascal

-Sd for delphi mode....

Required Delphi switches: -DMSWINDOWS -$H+

For Delphi 5,6,7 use -DDelphi

For Delphi 2005,2006,2007,2009,2010+ use the switch -DDELPHI2005

Regards,
Amine Moulay Ramdane.
http://pages.videotron.com/aminer/

[aminer10]

I wrote:
[...]
>for example an operation takes 10^9 second

I correct , i mean 10^-9 second.

Welcome: http://pages.videotron.com/aminer/

Regards,
Amine Moulay Ramdane.

[aminer10]

Hello,

I correct a typo:

It's the forward elimination that takes O(n^3) in the Gauss algorithm...

Please read again:

The Parallel iterative with relaxation method that i programmed here is
designed to be used to solve large sparse systems of linear equations
where the direct methods can exceed available machine memory and/or
be extremely time-consuming. for example the direct method of the
Gauss algorithm takes O(n^2) in the back substitution process and is
dominated by the O(n^3) forward elimination process, that means, if for
example an operation takes 10^-9 second and we have 1000 equations ,
the elimination process in the Gauss algorithm will takes 0.7 second, but
if we have 10000 equations in the system , the elimination process in the
Gauss algorithm will take 11 minutes !. This is why i have develloped for
you the Parallel Gauss-Seidel with relaxation iterative algorithm in Object Pascal,
that is very fast.

And welcome: http://pages.videotron.com/aminer/

Regards,
Amine Moulay Ramdane.

[aminer10]

Hello,

I have changed my notation to something like this:

pderivative(u)/pderivative(x1)

That means partial derivatives of function u with respect to x1....

Welcome:

http://pages.videotron.com/aminer/ParallelGaussSeidel/gsrp.htm

http://pages.videotron.com/aminer/

Regards,
Amine Moulay Ramdane.

[aminer10]

On http://www.lazarus.freepascal.org/index.php/topic,10971.0.html

Phil wrote:
>I moved {$IFDEF Unix}cthreads,{$ENDIF} to
>the beginning of the uses statement in gsr.pas

I have updated gsp.zip with that...

Phil wrote:
>Now it runs:
>The system may or may not converge...
>The system converge...
>The system solved...
>-2.1999999779999871E+0009 -2.0910889788668756E+0009 ->2.0490340859696247E+0009

That means that Parallel Gauss-Seidel with relaxation
algorithm is working on Windows and Mac OSX also :)

>I'm afraid I don't know enough about this to make any kind of
>educated guess about how it's used.
>Do you use this in your programming?

Parallel Gauss-Seidel with relaxation is of great importance
in partial differential equations, splines , Jackson Network
in Queuing theory etc. etc.

Welcome: http://pages.videotron.com/aminer/

Take care,

Amine Moulay Ramdane.