A characterization of positive quadrature formulae. (English) Zbl 0799.65020
It is shown that quasi-orthogonal polynomials that lead to positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal elements. Numerical results are not given.
Reviewer: S.Filippi (Gießen)
MSC:
| 65D32 | Numerical quadrature and cubature formulas |
| 41A55 | Approximate quadratures |
| 33C65 | Appell, Horn and Lauricella functions |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
Keywords:
quasi-orthogonal polynomials; positive quadrature formulae; characteristic polynomials; symmetric tridiagonal matrixReferences:
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