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Best quadrature formula on Sobolev class with Chebyshev weight

✍ Scribed by Congcong Xie

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
218 KB
Volume
214
Category
Article
ISSN
0377-0427

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πŸ“œ SIMILAR VOLUMES

On TurΓ‘n Quadrature Formulas for the Che
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As we know, the Chebyshev weight w(x)=(1&x 2 ) &1Γ‚2 has the property: For each fixed n, the solutions of the extremal problem dx for every even m are the same. This paper proves that the Chebyshev weight is the only weight having this property (up to a linear transformation).

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Making use of the connection between quadrature formulas on the unit circle and the interval [-1, 1] recently established in [1], explicit expressions for the nodes and the weights of the Gaussian formulas associated with rational modifications of the Chebyshev weight functions, are given. Some illu