As we know, the Chebyshev weight w(x)=(1&x 2 ) &1Γ2 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).
On Gaussian Quadrature Formulas for the Chebyshev Weight
β Scribed by Ying Guang Shi
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 126 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We present a new method for the approximation of Wiener integrals and provide an explicit error bound for a class F of smooth integrands. The purely deterministic algorithm is a sequence of quadrature formulas for the Wiener measure, where the knots are piecewise linear functions. It uses ideas of S
This paper is concerned with a Chebyshev quadrature rule for approximating one sided finite part integrals with smooth density functions. Our quadrature rule is based on the Chebyshev interpolation polynomial with the zeros of the Chebyshev polynomial T N+1 ({)&T N&1 (t). We analyze the stability an
We introduce new families of Gaussian-type quadratures for weighted integrals of exponential functions and consider their applications to integration and interpolation of bandlimited functions. We use a generalization of a representation theorem due to CarathΓ©odory to derive these quadratures. For