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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Weight functions for Chebyshev quadrature


Author: Yuan Xu
Journal: Math. Comp. 53 (1989), 297-302
MSC: Primary 65D32
MathSciNet review: 970703
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Abstract: In this paper, we investigate if the weight function $ {(1 - {x^2})^{ - 1/2}}R(x)$, where $ R(x)$ is a rational function of order (1,1), admits Chebyshev quadratures. Many positive examples are provided. In particular, we have proved that the answer is affirmative if $ R(x) = 1 + bx$, $ \vert b\vert < 0.27846 \ldots $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1989-0970703-2
PII: S 0025-5718(1989)0970703-2
Keywords: Chebyshev quadrature, weight function with property T
Article copyright: © Copyright 1989 American Mathematical Society