A characterization of positive quadrature formulae
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- by Yuan Xu PDF
- Math. Comp. 62 (1994), 703-718 Request permission
Abstract:
A positive quadrature formula with n nodes which is exact for polynomials of degree $2n - r - 1,0 \leq r \leq n$, 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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 62 (1994), 703-718
- MSC: Primary 41A55; Secondary 65D32
- DOI: https://doi.org/10.1090/S0025-5718-1994-1223234-0
- MathSciNet review: 1223234