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From Bani <>
Subject Re: [math] Q-R -decomposition
Date Sun, 21 May 2006 19:33:01 GMT
> > Beyond what is available in the API (Q and R), what exactly does the
> > QR Decomp "know" that makes solving easier?
> It has Q stored as a list of Householder vectors. Multiplying a matrix
> with Q or Q' that is stored in this format is not much more expensive
> than a normal matrix multiplication, but it's a lot more efficient
> when compared to first calculating an explicit form of Q and then
> multiplying. It might be better numerically too, but I cannot be sure.

Yes, QR is better, although it is more expensive to solve from scratch,
because of the ortogonality of the Q matrix.
It is particulary good for not very well conditioned systems. Sometimes you
can't even solve with LU, but you can with QR.


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