NDLI: On Stieltjes Polynomials and Gauss-Kronrod Quadrature

Content Provider	Scilit
Author	Peherstorfer, Franz
Copyright Year	1990
Description	Let D be a real function such that is analytic and for . Furthermore, put , , , and denote by the polynomial which is orthogonal on to ( denotes the set of polynomials of degree at most ) with respect to W. In this paper it is shown that for each sufficiently large n the polynomial (called the Stieltjes polynomial) of degree which is orthogonal on to with respect to the sign-changing function has simple zeros in and that the interpolation quadrature formula (called the Gauss-Kronrod quadrature formula) based on nodes which are the zeros of has all weights positive.
Related Links	https://www.ams.org/mcom/1990-55-192/S0025-5718-1990-1035940-8/S0025-5718-1990-1035940-8.pdf
Ending Page	664
Page Count	16
Starting Page	649
ISSN	00255718
e-ISSN	10886842
DOI	10.2307/2008439
Journal	Mathematics of Computation
Issue Number	192
Volume Number	55
Language	English
Publisher	Duke University Press
Publisher Date	1990-10-01
Access Restriction	Open
Subject Keyword	Logic Orthogonal Polynomials Orthogonal Polynomial
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory Computational Mathematics

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On Stieltjes Polynomials and Gauss-Kronrod Quadrature