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Thread Subject:
Large linear system

Subject: Large linear system

From: Frank

Date: 5 Jul, 2010 17:34:04

Message: 1 of 7

Hi,

I need to solve a linear system Ax=b with A being fat and sparse. However, the size of the matrix is very large. How can I solve x efficiently, such as using some iterative methods? Furthermore, are there any methods to solve the out of memory problem, for example, storing the nonzero elements of A?

Thanks a lot.

Frank

Subject: Large linear system

From: John D'Errico

Date: 5 Jul, 2010 17:52:04

Message: 2 of 7

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <i0t52c$dfo$1@fred.mathworks.com>...
> Hi,
>
> I need to solve a linear system Ax=b with A being fat and sparse. However, the size of the matrix is very large. How can I solve x efficiently, such as using some iterative methods? Furthermore, are there any methods to solve the out of memory problem, for example, storing the nonzero elements of A?
>

You need to spend some time reading the manual, if you
are solving large linear systems in matlab and you don't
know how to use sparse matrices in matlab.

help sparse
help slash

John

Subject: Large linear system

From: Marcus M. Edvall

Date: 5 Jul, 2010 21:39:27

Message: 3 of 7

Hi Frank,

TLSQR in the TOMLAB Base Module is usually quite efficient for this
problem type.

Best wishes, Marcus
Tomlab Optimization Inc.
http://tomsym.com/
http://tomdyn.com/

Subject: Large linear system

From: Matt J

Date: 5 Jul, 2010 22:30:08

Message: 4 of 7

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <i0t52c$dfo$1@fred.mathworks.com>...
> Hi,
>
> I need to solve a linear system Ax=b with A being fat and sparse. However, the size of the matrix is very large. How can I solve x efficiently, such as using some iterative methods? Furthermore, are there any methods to solve the out of memory problem, for example, storing the nonzero elements of A?
=============

See here for a recent related thread

http://www.mathworks.com/matlabcentral/newsreader/view_thread/285174

Subject: Large linear system

From: Steven Lord

Date: 6 Jul, 2010 02:47:08

Message: 5 of 7


"Frank " <allinone_2003@yahoo.com.hk> wrote in message
news:i0t52c$dfo$1@fred.mathworks.com...
> Hi,
>
> I need to solve a linear system Ax=b with A being fat and sparse. However,
> the size of the matrix is very large. How can I solve x efficiently, such
> as using some iterative methods? Furthermore, are there any methods to
> solve the out of memory problem, for example, storing the nonzero elements
> of A?

There's a list of a few sparse iterative methods in the help text for the
sparse functions:

help sparfun

Most require the coefficient matrix to be square, but LSQR does not.

--
Steve Lord
slord@mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

Subject: Large linear system

From: Peter

Date: 22 Apr, 2011 23:44:05

Message: 6 of 7

Hi, in regards to the above thread, does anyone know the best way to solve a 1e6 x 1e6 sparse non symmetric system? I am using mldivide (it takes around ~2 min)? Are there any iterative methods that are much faster, and if so, how can I quickly generate the preconditioner (using ilu seems to be slow)?

Thanks,
Peter

"Steven Lord" <slord@mathworks.com> wrote in message <i0u5fc$7lb$1@fred.mathworks.com>...
>
> "Frank " <allinone_2003@yahoo.com.hk> wrote in message
> news:i0t52c$dfo$1@fred.mathworks.com...
> > Hi,
> >
> > I need to solve a linear system Ax=b with A being fat and sparse. However,
> > the size of the matrix is very large. How can I solve x efficiently, such
> > as using some iterative methods? Furthermore, are there any methods to
> > solve the out of memory problem, for example, storing the nonzero elements
> > of A?
>
> There's a list of a few sparse iterative methods in the help text for the
> sparse functions:
>
> help sparfun
>
> Most require the coefficient matrix to be square, but LSQR does not.
>
> --
> Steve Lord
> slord@mathworks.com
> comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
> To contact Technical Support use the Contact Us link on
> http://www.mathworks.com
>

Subject: Large linear system

From: Matt J

Date: 23 Apr, 2011 03:57:08

Message: 7 of 7

"Peter" wrote in message <iot3s5$9k3$1@fred.mathworks.com>...
> Hi, in regards to the above thread, does anyone know the best way to solve a 1e6 x 1e6 sparse non symmetric system? I am using mldivide (it takes around ~2 min)? Are there any iterative methods that are much faster, and if so, how can I quickly generate the preconditioner (using ilu seems to be slow)?
==================

It depends on a million things, e.g., how sparse the matrix is, how diagonally concentrated it is, etc...

See here for some discussion

http://www.mathworks.com/matlabcentral/newsreader/view_thread/285174

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