<br><br><div class="gmail_quote">On Mon, May 3, 2010 at 1:45 AM, Soeren Gebbert <span dir="ltr"><<a href="mailto:soerengebbert@googlemail.com">soerengebbert@googlemail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Hello,<br>
LU is used to solve the linear equation system, because the matrix is<br>
not positive definite. There is a zero at the diagonal. You can try to<br>
sort the rows and cols, but i'm not sure if the matrix will get<br>
positive definite. Maybe an LDL decomposition can be used instead of<br>
LU.<br>
I have tried to solve the linear equation system with a parallele<br>
BiCGStab algorithm, but most of the time the linear equation system is<br>
of very bad condition, so the BiCGStab solver fails. An LU algorithm<br>
with pivoting is needed.<br>
<br>
Hence, reordering rows and cols to avoid a zero at the diagonal and<br>
parallel LDL decomposition may be the best choice.<br>
<br></blockquote><div><br></div><div><br></div><div><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; border-collapse: collapse; ">I believe you meant LDU decomposition here. </span></div>
<div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
The RST Matrix looks most of the time like this:<br>
<br>
0.0 1.0 1.0 1.0<br>
1.0 -0.1 3.0 2.5<br>
1.0 3.0 -0.1 2.2<br>
1.0 2.5 2.2 -0.1<br>
<br>
I do not understand the matrix assembling algorithm, nor the spline<br>
interpolation algorithm, so i don't know how the zero at the diagonal<br>
can be prevented on algorithm side.<br>
<br></blockquote><div><br></div><div><br></div><div><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; border-collapse: collapse; ">There are many people out there in grass-dev list who understand these. I request them to please reply. </span></div>
<div><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; border-collapse: collapse; "><br></span></div><div><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; border-collapse: collapse; "><br>
</span></div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Best regards<br>
Soeren<br>
<br>
2010/5/2 Abhishek Shukla <<a href="mailto:abhishekiiith@gmail.com">abhishekiiith@gmail.com</a>>:<br>
<div><div></div><div class="h5">> Hi list,<br>
> I want to ask why LU decomposition has been used for matrix solving in RST<br>
> library when matrix being solved is symmetric. I am planning to solve it<br>
> using Cholesky decomposition.<br>
> I want to confirm with grass developers that there is no issue if I solve it<br>
> using Cholesky decomposition. My goal is not to change current serial<br>
> implementation, I am implementing (started, at least) v.surf.rst on GPU and<br>
> planning to use Cholesky instead of LU as it is expected to show better<br>
> performance over LU.<br>
><br>
><br>
> Please someone confirm that it is okay to solve matrix using Cholesky<br>
> decomposition.<br>
><br>
><br>
> ---<br>
> Abhishek Shukla<br>
> Center for Security, Theory And Algorithm Research (CSTAR)<br>
> International Institute of Information Technology<br>
> Hyderabad<br>
> India<br>
> <a href="http://www.iiit.ac.in/" target="_blank">http://www.iiit.ac.in/</a><br>
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</blockquote></div><br>