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matrix ( the singular values of which are the shifted zeroes of the n-th orthogonal polynomial ) is a 10-years old unpublished result ...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