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Re: full QR decomposition

• To: mathgroup at smc.vnet.net
• Subject: [mg51689] Re: [mg51645] full QR decomposition
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Fri, 29 Oct 2004 03:39:22 -0400 (EDT)
• References: <200410280343.XAA09703@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Oct 27, 2004, at 11:43 PM, Jan Schmedes wrote:

> Dear group,
>
> i have the following problem. For a given a NxM (e.g. 3000x600) matrix 
> A i
> get a matrix Q (MxN) and R (MxM) after the QRDecomposition. But i would
> like to get the full decomposition with a matrix QF (NxN) and RF (NxM) 
> where RF
> contains only zero lines below the line with index M. I'm especially
> interrested in the last N-M lines in QF which create the zero lines in 
> RF.
> At the moment i use QRDecomposition and append then N-M random lines to
> the matrix Q. With this new matrix i go into the routine GramSchmidt 
> and extract the last N-M
> lines from the result. But this is very slow and i'm not sure if it 
> will
> always work?

This will not always work because there is a very small probability 
that the space spanned by the entries you've added overlaps the space 
spanned by Q.

> Are there any suggestions or hints?

What you are after is the basis of the null space of your original 
matrix.  If you use NullSpace then the resulting vectors span the same 
space as the "missing" rows of Q.

Regards,

Ssezi

• References:
  • full QR decomposition
    • From: Jan Schmedes <schmedes@rz.uni-potsdam.de>