BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-91-06
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: How to generate unknown orthogonal polynomials out of known
               orthogonal polynomials
        TYPE:: Manuscript
      AUTHOR:: Golub, Gene H.
      AUTHOR:: Fischer, Bernd
        DATE:: November 1991
       PAGES:: 22
    ABSTRACT:: We consider the problem of generating the three-term
               recursion coefficients of orthogonal polynomials for a weight
               function $v(t) = r(t)w(t)$, obtained by modifying a given
               weight function $w$ by a rational function $r$. Algorithms
               for the construction of the orthogonal polynomials for the
               new weight $v$ in terms of those for the old weight $w$ are
               presented. All the methods are based on modified moments. As
               applications we present Gaussian quadrature rules for
               integrals in which the integrand has singularities close to
               the interval of integration, and the generation of orthogonal
               polynomials for the (finite) Hermite weight $e^{-t^{2}}$,
               supported on a finite interval [$-b,b$].
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-91-06