## Linear combinations of orthogonal polynomials generating positive quadrature formulas

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- by Franz Peherstorfer PDF
- Math. Comp.
**55**(1990), 231-241 Request permission

## Abstract:

Let ${p_k}(x) = {x^k} + \cdots$, $k \in {{\mathbf {N}}_0}$, be the polynomials orthogonal on $[ - 1, + 1]$ with respect to the positive measure $d\sigma$. We give sufficient conditions on the real numbers ${\mu _j}$, $j = 0, \ldots ,m$, such that the linear combination of orthogonal polynomials $\sum _{j = 0}^m{\mu _j}{p_{n - j}}$ has*n*simple zeros in $( - 1, + 1)$ and that the interpolatory quadrature formula whose nodes are the zeros of $\sum _{j = 0}^m{\mu _j}{p_{n - j}}$ has positive weights.

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## Additional Information

- © Copyright 1990 American Mathematical Society
- 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