A characterization of positive quadrature formulae

Author:
Yuan Xu

Journal:
Math. Comp. **62** (1994), 703-718

MSC:
Primary 41A55; Secondary 65D32

MathSciNet review:
1223234

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Abstract | References | Similar Articles | Additional Information

Abstract: A positive quadrature formula with *n* nodes which is exact for polynomials of degree , is based on the zeros of certain quasi-orthogonal polynomials of degree *n*. We show that the quasi-orthogonal 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/S0025-5718-1994-1223234-0

Keywords:
Quadrature formula,
quasi-orthogonal polynomial,
tridiagonal matrix

Article copyright:
© Copyright 1994
American Mathematical Society