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Parallel implementation of Jacobi with relaxation Linear Algebraic System Solver version 1.0

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  Parallel implementation of Jacobi with relaxation Linear Algebraic System Solver version 1.0 "aminer" <aminer@videotron.ca> - 2012-06-09 20:33 -0500
    Re: Parallel implementation of Jacobi with relaxation Linear Algebraic System Solver version 1.0 "aminer" <aminer@videotron.ca> - 2012-06-10 10:54 -0500
    Re: Parallel implementation of Jacobi with relaxation Linear Algebraic System Solver version 1.0 "aminer" <aminer@videotron.ca> - 2012-06-10 16:13 -0500

#924 — Parallel implementation of Jacobi with relaxation Linear Algebraic System Solver version 1.0

Hello all,

Parallel implementation of Jacobi with relaxation Linear Algebraic System 
Solver version 1.0


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 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 
Jacobi 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 Jacobi with 
relaxation iterative algorithm in Object Pascal, that is very fast.
Please read more here: 
http://pages.videotron.com/aminer/ParallelJacobiWithRelaxation/pjr.htm
Please look at test.pas example inside the zip file, compile and execute 
it...



You can download Parallel implementation of Jacobi with relaxation Linear 
Algebraic System Solver version 1.0 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....

-dUnix for Linux,MacOSX etc.

Required Delphi switches: -DMSWINDOWS -$H+ -DDelphi


Thank you.
Amine Moulay Ramdane.

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#925

Hello,

If you want to compile Parallel implementation of Jacobi with relaxation
Linear System Solver version 1.0 to the Win64 system, just set the CPU=64 in
the defines.inc.

In my Parallel algorithm i use a factor 'lambda' that is assigned a value
between 0 and 2 , if this factor is set between 0 and 1 we call it 
underrelaxation
and is typically employed to make nonconvergent system converge or to hasten
convergence by dampening out oscillations.

If the value of lambda is comprised between 1 and 2, we call it 
overrelaxation,
and is designed to 'accelerate' the convergence of an already convergent 
system.
The approach is also called successive or simultaneous overrelaxation or 
SOR.
And a theorem due to Kahan shows that SOR fails to converge if it is outside 
the
interval [0,2] .

Now i have played with the lambda and i have noticed that when you set size
of the matrix to a number, you have to count the number of digits in this 
number,
for example if the size of the matrix is 2000 , it means the size is  4 
digits. Now
i have noticed that to make the system converge you have to set the lambda
to the same number of digits than the size or set it to the number of digits 
than
the size of the matrix + 1.

Example if the size is 2000 you have to set the the number of digits before 
the comma
and after the comma to the same number of digits than the size or  set it to 
the number of digits
of the size of the matrix +1 , that means that in this example to make the 
system
converge set the lambda to 0,001 or 0,0001.

and if the size of the matrix is 3 , set the lambda to 1 or 0,1 to make the 
system converge.




Thank you.
Amine Moulay Ramdane.








"aminer" <aminer@videotron.ca> wrote in message 
news:jr0q0v$png$1@dont-email.me...
>
>
> Hello all,
>
> Parallel implementation of Jacobi with relaxation Linear Algebraic System 
> Solver version 1.0
>
>
> Description:
>
> The Parallel iterative with relaxation method that i programmed here is 
> designed to be used to solve large sparse systems of linear equations 
> where the direct methods can exceed available machine memory and/or be 
> extremely time-consuming. for example the direct method of the Gauss 
> algorithm takes O(n^2) in the back substitution process and is dominated 
> by the O(n^3) forward elimination process, that means, if for example an 
> operation takes 10^-9 second and we have 1000 equations , the elimination 
> process in the Jacobi algorithm will takes 0.7 second, but if we have 
> 10000 equations in the system , the elimination process in the Gauss 
> algorithm will take 11 minutes !. This is why i have develloped for you 
> the Parallel Jacobi with relaxation iterative algorithm in Object Pascal, 
> that is very fast.
> Please read more here: 
> http://pages.videotron.com/aminer/ParallelJacobiWithRelaxation/pjr.htm
> Please look at test.pas example inside the zip file, compile and execute 
> it...
>
>
>
> You can download Parallel implementation of Jacobi with relaxation Linear 
> Algebraic System Solver version 1.0 from:
>
> http://pages.videotron.com/aminer/
>
>
> Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/
>
> Operating Systems: Win , Linux and Mac (x86).
>
> Required FPC switches: -O3 -Sd -dFPC -dWin32 -dFreePascal
>
> -Sd for delphi mode....
>
> -dUnix for Linux,MacOSX etc.
>
> Required Delphi switches: -DMSWINDOWS -$H+ -DDelphi
>
>
> Thank you.
> Amine Moulay Ramdane.
>
>
>
> 

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#926

Hello,

Red-black Gauss-Seidel converges twice as fast as Jacobi,
but there are twice as many parallel steps, so the same in practice

http://www.cs.berkeley.edu/~skamil/cs267/slides/lecture12_structured_hds08.pdf




Thank you.
Amine Moulay Ramdane.





"aminer" <aminer@videotron.ca> wrote in message 
news:jr0q0v$png$1@dont-email.me...
>
>
> Hello all,
>
> Parallel implementation of Jacobi with relaxation Linear Algebraic System 
> Solver version 1.0
>
>
> Description:
>
> The Parallel iterative with relaxation method that i programmed here is 
> designed to be used to solve large sparse systems of linear equations 
> where the direct methods can exceed available machine memory and/or be 
> extremely time-consuming. for example the direct method of the Gauss 
> algorithm takes O(n^2) in the back substitution process and is dominated 
> by the O(n^3) forward elimination process, that means, if for example an 
> operation takes 10^-9 second and we have 1000 equations , the elimination 
> process in the Jacobi algorithm will takes 0.7 second, but if we have 
> 10000 equations in the system , the elimination process in the Gauss 
> algorithm will take 11 minutes !. This is why i have develloped for you 
> the Parallel Jacobi with relaxation iterative algorithm in Object Pascal, 
> that is very fast.
> Please read more here: 
> http://pages.videotron.com/aminer/ParallelJacobiWithRelaxation/pjr.htm
> Please look at test.pas example inside the zip file, compile and execute 
> it...
>
>
>
> You can download Parallel implementation of Jacobi with relaxation Linear 
> Algebraic System Solver version 1.0 from:
>
> http://pages.videotron.com/aminer/
>
>
> Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/
>
> Operating Systems: Win , Linux and Mac (x86).
>
> Required FPC switches: -O3 -Sd -dFPC -dWin32 -dFreePascal
>
> -Sd for delphi mode....
>
> -dUnix for Linux,MacOSX etc.
>
> Required Delphi switches: -DMSWINDOWS -$H+ -DDelphi
>
>
> Thank you.
> Amine Moulay Ramdane.
>
>
>
> 

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