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MathGroup Archive 2003

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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>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • 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[1]:=
> *)
> 
> SeedRandom[1];
> A = Table[Random[],{200},{200}];
> B = Table[Random[],{200},{10}];
> LinearSolve[A,B];//Timing
> 
> (*
> Out[1]=
> {0.03 Second,Null}
> 
> 2.) lots slower:
> input matrices are rectangular {201,200}, {201,10} - Overdetermined
> 
> In[2]:=
> *)
> 
> SeedRandom[1];
> A = Table[Random[],{201},{200}];
> B = Table[Random[],{201},{10}];
> LinearSolve[A,B];//Timing
> 
> (*
> Out[2]=
> {0.761 Second,Null}
> 
> In[3]:=
> 0.761/.03
> 
> Out[3]=
> 25.3667
> ***************************)
> 
> I expect more difficult computation, but not so difficult.
> 
> Where is problem? Exists some option Method for LinerSolve[] or another
> trick?
> 
> Thank in advance for all your help.
> Best regards,
>     Petr.


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