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Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0

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"The Conjugate Gradient Method is the most prominent iterative method for 
solving sparse systems of linear equations. Unfortunately, many textbook 
treatments of the topic are written with neither illustrations nor 
intuition, and their victims can be found to this day babbling senselessly 
in the corners of dusty libraries. For this reason, a deep, geometric 
understanding of the method has been reserved for the elite brilliant few 
who have painstakingly decoded the mumblings of their forebears. Conjugate 
grandient is the most popular iterative method for solving large systems of 
linear equations. CG is effective for systems of the form A.x = b
where x is an unknown vector,    b is a known vector, A and is a known, 
square, symmetric, positive-definite
(or positive-indefinite) matrix. These systems arise in many important 
settings, such as finite difference and finite element methods for solving 
partial differential equations, structural analysis, circuit analysis, and 
math homework."



Thank you.
Amine Moulay Ramdane.


"aminer" <aminer@videotron.ca> wrote in message 
news:jrd0mp$h8o$1@dont-email.me...
>
> Hello,
>
>
> Parallel implementation of Conjugate Gradient Linear System Solver 1.0
>
>
> Description:
>
> The Parallel implementation of Conjugate Gradient Linear System Solver 
> that i programmed here is designed to be used to solve large sparse 
> systems of linear equations where the direct methods can exceed available 
> machine memory and/or be extremely time-consuming. for example the direct 
> method of the Gauss algorithm takes O(n^2) in the back substitution 
> process and is dominated by the O(n^3) forward elimination process, that 
> means, if for example an operation takes 10^-9 second and we have 1000 
> equations , the elimination process in the Gauss algorithm will takes 0.7 
> second, but if we have 10000 equations in the system , the elimination 
> process in the Gauss algorithm will take 11 minutes !. This is why i have 
> develloped for you the Parallel implementation of Conjugate Gradient 
> Linear System Solver in Object Pascal, that is very fast.
>
> Jacobi serial complexity is O(N^2) and Conjugate gradient serial 
> complexity = O(N^3/2).
>
> You can download Parallel implementation of Conjugate Gradient Linear 
> System Solver 1.0 from:
>
> http://pages.videotron.com/aminer/
>
> Please look at the test.pas example inside the zip file, compile and 
> execute it...
>
> Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/
>
> Operating Systems: Win , Linux and Mac (x86).
>
> Note: to be able to port to Linux and Mac OSX you have to compile the 
> dynamic libraries...
>
> Required FPC switches: -O3 -Sd -dFPC -dWin32 -dFreePascal
>
> -Sd for delphi mode....
>
> -dUnix for Linux,MacOSX etc.
>
> Required Delphi switches: -DMSWINDOWS -$H+ -DDelphi
>
> And inside defines.inc you have two defines:
>
> {$DEFINE CPU32} for 32 bits systems
> {$DEFINE CPU64} for 64 bits systems
>
>
>
> Thank you.
> Amine Moulay Ramdane.
>
>
> 

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Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 11:41 -0500
  Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 11:47 -0500
  Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 12:03 -0500
    Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 12:13 -0500
  Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 12:54 -0500
  Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 15:56 -0500
  Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-14 17:22 -0500
  Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0 "aminer" <aminer@videotron.ca> - 2012-06-15 09:21 -0500

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