🚀 go-pugleaf

In article <376C787E.939C192B@kings.uq.edu.au>, c.armour@uq.net.au wrote�:

: Hi,
: 
: I need to write a paper on the use of Singular value Decomposition in
: numerical Algebra for numerical maths.  The main problem I'm having is
: finding a paper or the sort which describes the svd w.r.t other
: algorithms interms of performance and various problems.  
: 
: I realise SVD's are great for overconditioned problmes, but how are they
: better than say a QR factorization.  As far as I can figure, alot of
: algorithms use QR and the sort to compute the svd.  what about w.r.t
: eigen value problems.
: 
: In short, I have a lot of info telling me that SVD's are great for
: overconditioned systems and least squares but not much else.  Is this
: the only use of SVD's? for least squares style problems???
: 

Not many people know it but all orthogonal polynomials satisfy coupled
2-terms recurrences, so that their zeros are related with the singular
values of a bidiagonal matrix ; SVD is therefore an essential tool in
the numerical construction of Gaussian quadratures.

Bernard Danloy