🚀 go-pugleaf

In article <pecora-2106990936270001@pecora7600.nrl.navy.mil>,
pecora@zoltar.nrl.navy.mil (Louis M. Pecora) wrote �:

: In article <danloy-2106991346450001@quadra.anma.ucl.ac.be>,
: danloy@anma.ucl.ac.be (Bernard Danloy) wrote:
: 
:  > 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 ;
: 
: Hi Bernard,
: 
: This is very interesting.  Can you point to a reference where I can read
: more?  Thanks.
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Sorry, i don't have many pointers ...

The coupled recurrences are the system (2.6) in a paper of mine in Math.
Comp. vol. 27 ( 1973 ) p. 863

Rewriting the system by means of a bidiagonal matrix ( the singular values
of which are the shifted zeroes of the n-th orthogonal polynomial ) is a
10-years old unpublished result ...

But recently, similar results have been obtained independently by Dirk
Laurie and i believe you should find something in a coming issue of JCAM.

Bernard Danloy