# [Numpy-discussion] Numpy and iterative procedures

Nils Wagner nwagner@iam.uni-stuttgart...
Thu Feb 15 10:46:05 CST 2007

```Geoffrey Zhu wrote:
> Thanks Chuck.
>
> I am trying to use Successive Over-relaxation to solve linear
> equations defined by M*v=q.
>
AFAIK, splitting methods are not the best methods to solve a system of
linear equations, iteratively.
What can be said about your coefficient matrix M ? Is it spd (symmetric
positive definite) ?
In that case I suggest to use cg.

Anyway, you may try the following solvers which are available in scipy

Iterative linear systems solutions

cg         --- Conjugate gradient (symmetric systems only)
qmr        --- Quasi-minimal residual
gmres      --- Generalized minimal residual

Nils

> There are several goals:
>
> 1. Eventually (in production) I need it to be fast.
> 2. I am playing with the guts of the algorithm for now, to see how it
> works. that means i need some control for now.
> 3. Even in production, there is a chance i'd like to have the ability
> to tinker with the algorithm.
>
>
> ------------------------------------------------------------------------
> *From:* numpy-discussion-bounces@scipy.org
> [mailto:numpy-discussion-bounces@scipy.org] *On Behalf Of *Charles R
> Harris
> *Sent:* Thursday, February 15, 2007 10:11 AM
> *To:* Discussion of Numerical Python
> *Subject:* Re: [Numpy-discussion] Numpy and iterative procedures
>
>
>
> On 2/15/07, *Geoffrey Zhu* <gzhu@peak6.com <mailto:gzhu@peak6.com>>
> wrote:
>
>     Hi,
>
>     I am new to numpy. I'd like to know if it is possible to code
>     efficient
>     iterative procedures with numpy.
>
>     Specifically, I have the following problem.
>
>     M is an N*N matrix. Q is a N*1 vector. V is an N*1 vector I am
>     trying to
>     find iteratively from the initial value V_0. The procedure is
>     simply to
>     calculate
>
>     V_{n+1}[i]=3D1/M[I,i]*(q[i]-
>     (M[i,1]*v_{n+1}[1]+M[I,2]*v_{n+1}[2]+..+M[i,i-1]*v_{n+1}[i-1]) -
>     (M[I,i+1]*v_{n}[i+1]+M[I,i+2]*v_{n}[i+2]+..+M[I,N]*v_{n}[N]))
>
>     I do not see that this is something that can esaily be vectorized, is
>     it?
>
>
> I think it would be better if you stated what the actual problem is.
> Is it a differential equation, for instance. That way we can determine
> what the problem class is and what algorithms are available to solve it.
>
> Chuck
>
>
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```