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Re: Parallel implementation of Conjugate Gradient Linear System Solver 1.0

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"In the method of conjugate gradients the residuals are not used
as search directions, as in the steepest decent method, cause searching
can require a large number of iterations as the residuals zig zag towards
the minimum value for ill-conditioned matrices. But instead conjugate
gradient method uses the residuals as a basis to form conjugate search
directions . In this manner, the conjugated gradients (residuals) form a
basis of search directions to minimize the quadratic function f(x) and
to achieve result of dim(N) convergence."



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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