[GRASS-dev] Re: v.surf.rst

[Abhishek Shukla]

On Mon, May 3, 2010 at 1:45 AM, Soeren Gebbert <soerengebbert at googlemail.com
> wrote:

> Hello,
> LU is used to solve the linear equation system, because the matrix is
> not positive definite. There is a zero at the diagonal. You can try to
> sort the rows and cols, but i'm not sure if the matrix will get
> positive definite. Maybe an LDL decomposition can be used instead of
> LU.
> I have tried to solve the linear equation system with a parallele
> BiCGStab algorithm, but most of the time the linear equation system is
> of very bad condition, so the BiCGStab solver fails. An LU algorithm
> with pivoting is needed.
>
> Hence, reordering rows and cols to avoid a zero at the diagonal and
> parallel LDL decomposition may be the best choice.
>
>

I believe  you meant LDU decomposition here.



> The RST Matrix looks most of the time like this:
>
> 0.0  1.0  1.0  1.0
> 1.0 -0.1  3.0  2.5
> 1.0  3.0 -0.1  2.2
> 1.0  2.5  2.2 -0.1
>
> I do not understand the matrix assembling algorithm, nor the spline
> interpolation algorithm, so i don't know how the zero at the diagonal
> can be prevented on algorithm side.
>
>

There are many people out there in grass-dev list who understand these. I
request them to please reply.




> Best regards
> Soeren
>
> 2010/5/2 Abhishek Shukla <abhishekiiith at gmail.com>:
> > Hi list,
> > I want to ask why LU decomposition has been used for matrix solving in
> RST
> > library when matrix being solved is symmetric. I am planning to solve it
> > using Cholesky decomposition.
> > I want to confirm with grass developers that there is no issue if I solve
> it
> > using Cholesky decomposition. My goal is not to change current serial
> > implementation, I am implementing  (started, at least) v.surf.rst on GPU
> and
> > planning to use Cholesky instead of LU as it is expected to show better
> > performance over LU.
> >
> >
> > Please someone confirm that it is okay to solve matrix using Cholesky
> > decomposition.
> >
> >
> > ---
> > Abhishek Shukla
> > Center for Security, Theory And Algorithm Research (CSTAR)
> > International Institute of Information Technology
> > Hyderabad
> > India
> > http://www.iiit.ac.in/
> > _______________________________________________
> > grass-dev mailing list
> > grass-dev at lists.osgeo.org
> > http://lists.osgeo.org/mailman/listinfo/grass-dev
> >
>
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