A characterization of positive quadrature formulae
Author:
Yuan Xu
Journal:
Math. Comp. 62 (1994), 703718
MSC:
Primary 41A55; Secondary 65D32
MathSciNet review:
1223234
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Abstract: A positive quadrature formula with n nodes which is exact for polynomials of degree , is based on the zeros of certain quasiorthogonal polynomials of degree n. We show that the quasiorthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal entries. As a consequence, for a fixed n, every positive quadrature formula is a Gaussian quadrature formula for some nonnegative measure.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199412232340
PII:
S 00255718(1994)12232340
Keywords:
Quadrature formula,
quasiorthogonal polynomial,
tridiagonal matrix
Article copyright:
© Copyright 1994
American Mathematical Society
