       Re: LinearSolve - consumption time for square and rectangular matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg44027] Re: LinearSolve - consumption time for square and rectangular matrices
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 18 Oct 2003 03:12:20 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <bmodpc\$hrf\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

you should use a QR factorisation for nearly singular
systems.

And you should not get a solution at all for a singular
system by LinearSolve[]

Regards
Jens

Petr Kujan wrote:
>
> Hello MathGroup,
>
> I don't know about big difference in consumption time in LinearSolve[]
> with square/rectangular matrices.
>
> I am using Mathematica 5.0, PC: Duron 750, W2k
>
> Here is example.
> (***************************
> 1.) very fast:
> input matrices are square {200,200} and rectangular {200,10}
>
> In:=
> *)
>
> SeedRandom;
> A = Table[Random[],{200},{200}];
> B = Table[Random[],{200},{10}];
> LinearSolve[A,B];//Timing
>
> (*
> Out=
> {0.03 Second,Null}
>
> 2.) lots slower:
> input matrices are rectangular {201,200}, {201,10} - Overdetermined
>
> In:=
> *)
>
> SeedRandom;
> A = Table[Random[],{201},{200}];
> B = Table[Random[],{201},{10}];
> LinearSolve[A,B];//Timing
>
> (*
> Out=
> {0.761 Second,Null}
>
> In:=
> 0.761/.03
>
> Out=
> 25.3667
> ***************************)
>
> I expect more difficult computation, but not so difficult.
>
> Where is problem? Exists some option Method for LinerSolve[] or another
> trick?
>