Re: [eigen] HELP : SVD too slow

[Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx>]

On 06/29/2012 10:29:06 AM, Gaurav Gupta wrote:
> The maximum dimension is 8 x 6, if bordered matrix approach can  
> improve
> speed, I am very much interested

So, you're interested in cases where such an 8 x 6 matrix doesn't have  
full column rank.
If the rank defect is about 1 or 2, bordered system could be a speed up.

For a first impression you might have a look at


W. Govaerts, J.D. Pryce  "Mixed block elimination for linear systems  
with wider borders"
IMA J. Numer. Anal. 13 (1993), pp 161-180

or chapter 3 in

http://books.google.de/books?id=I1M5ZISH9SsC&pg=PA350&lpg=PA350&dq=Govaerts+Mixed+block+elimination+for+linear+systems+with+wider+borders+IMA+J+Numer.+Anal.&source=bl&ots=ddaG3Oecid&sig=IqMi-Gth07WFxM5iOp8Rflz9awQ&hl=de&sa=X&ei=tWztT-aPFYjm4QS34uzuDQ&sqi=2&ved=0CEYQ6AEwAg#v=onepage&q=Govaerts%20Mixed%20block%20elimination%20for%20linear%20systems%20with%20wider%20borders%20IMA%20J%20Numer.%20Anal.&f=false

FORTRAN software is here
http://www.netlib.org/linalg/bemw.tgz

If you like I can send you my Scilab application which tries to find
a parameter-dependend matrix of prescribed rank (defect).

Helmut.

> On Fri, Jun 29, 2012 at 1:55 PM, Helmut Jarausch <
> jarausch@xxxxxxxxxxxxxxxxxxx> wrote:
>
> > On 06/29/2012 10:21:25 AM, Gaurav Gupta wrote:
> >
> >> I opted for eigen3 to improve speed of my program than on MATLAB,  
> but it
> >> is
> >> taking more time than MATLAB.
> >> I am using JacobiSVD for calculating nullspace, which is taking  
> most of
> >> the
> >> time, any suggestions for improving speed,
> >> or any way to implement SVD faster.
> >>
> >>
> >
> > What dimension will the nullspace have?
> >
> > If not too large you could consider using a bordered matrix  
> approach.
> > If you're interested I'll be happy to give to some references an  
> even a
> > Scilab implementation
> > of this.
> >
> > Helmut.
> >
> >
> >