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cholesky conjugated gradient method
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| Hi all,
Could anyone explain to me about cholesky conjugated gradient method?
If I'm not mistaken it's an iterative algorithm to find solution of
system of linear equations..
Thanks
Bowo
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| Brooks Moses 2006-01-24, 3:57 am |
| bowo wrote:
> Hi all,
> Could anyone explain to me about cholesky conjugated gradient method?
> If I'm not mistaken it's an iterative algorithm to find solution of
> system of linear equations..
Yes, it is, although it's properly the "Cholesky conjugate gradient"
method. I'd hoped that putting the correct spelling into Google would
find some convenient references, but it doesn't really. Looking through
them does find enough information to answer your question, though....
First, the two-paragraph introduction to the Cholesky conjugate gradient
method in http://www-db.stanford.edu/TR/CS-TR-90-1330.html (look at the
pdf linked from there) usefully points out that the "Cholesky conjugate
gradient" method is really just the ordinary conjugate gradient method
with the Cholesky decomposition used as a preconditioner.
That implies that perhaps it would be more useful to just look for
information on "conjugate gradient" and "Cholesky decomposition"
separately. And that does turn up rather more stuff; the MathWorld
descriptions of conjugate gradient methods and Cholesky decompositions
should be a good start:
http://mathworld.wolfram.com/Conjug...ientMethod.html
http://mathworld.wolfram.com/CholeskyDecomposition.html
Hope this helps,
- Brooks
--
The "bmoses-nospam" address is valid; no unmunging needed.
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| Pierre Asselin 2006-01-24, 7:02 pm |
| Brooks Moses <bmoses-nospam@cits1.stanford.edu> wrote:
> bowo wrote:
[color=darkred]
> Yes, it is, although it's properly the "Cholesky conjugate gradient"
*Incomplete* Cholesky conjugate gradient. Otherwise there's no point!
> [ ... ] http://www-db.stanford.edu/TR/CS-TR-90-1330.html [ ... ]
Indeed.
--
pa at panix dot com
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| Victor Eijkhout 2006-01-26, 7:03 pm |
| Pierre Asselin <pa@see.signature.invalid> wrote:
>
> *Incomplete* Cholesky conjugate gradient. Otherwise there's no point!
Incomplete Cholesky preconditioned conjugate gradient method.....
Victor.
--
Victor Eijkhout -- eijkhout at tacc utexas edu
ph: 512 471 5809
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