From: danloy@anma.ucl.ac.be (Bernard Danloy)
Subject: Re: Singular Value Decomposition
Date: Mon, 21 Jun 1999 16:59:30 +0200
Newsgroups: sci.math.num-analysis,aus.mathematics
Keywords: all orthogonal polynomials satisfy coupled 2-terms recurrences
In article ,
pecora@zoltar.nrl.navy.mil (Louis M. Pecora) wrote :
: In article ,
: 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10-years old unpublished result ...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