Linear combinations of orthogonal polynomials generating positive quadrature formulas

Author:
Franz Peherstorfer

Journal:
Math. Comp. **55** (1990), 231-241

MSC:
Primary 65D32; Secondary 41A55, 42C05

DOI:
https://doi.org/10.1090/S0025-5718-1990-1023052-9

MathSciNet review:
1023052

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , , be the polynomials orthogonal on with respect to the positive measure . We give sufficient conditions on the real numbers , , such that the linear combination of orthogonal polynomials has *n* simple zeros in and that the interpolatory quadrature formula whose nodes are the zeros of has positive weights.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-1023052-9

Keywords:
Quadrature formula,
positive weights,
orthogonal polynomials,
zeros

Article copyright:
© Copyright 1990
American Mathematical Society