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New interpolatory quadrature formulae with Chebyshev abscissae

✍ Scribed by Sotirios E. Notaris

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
747 KB
Volume
94
Category
Article
ISSN
0377-0427

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✦ Synopsis

We study interpolatory quadrature formulae, relative to the Legendre weight function on [-1, 1], having as nodes the zeros of any one of the four Chebyshev polynomials of degree n plus one of the points 1 or -1. In particular, we derive explicit formulae for the weights and examine their positivity, we determine the precise degree of exactness, we obtain asymptotically optimal error bounds, and we examine the definiteness of these quadrature formulae. In addition, we establish their convergence for Riemann integrable functions on [-1, 1] as well as for functions having a monotonic singularity at -1 or 1. (~) 1998 Elsevier Science B.V. All rights reserved.

πŸ“œ SIMILAR VOLUMES

Interpolatory quadrature formulae with C
Interpolatory quadrature formulae with Chebyshev abscissae of the third or fourth kind
✍ Sotirios E. Notaris πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 755 KB

We consider interpolatory quadrature formulae, relative to the Legendre weight function on [-1, 1], having as nodes the zeros of the nth-degree Chebyshev polynomial of the third or fourth kind. Szeg5 has shown that the weights of these formulae are all positive. We derive explicit formulae for the w