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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • MathSciNet review: 1023052