منابع مشابه
On Chebyshev-Type Quadratures
According to a result of S. N. Bernstein, «-point Chebyshev quadrature formulas, with all nodes real, do not exist when n = 8 or n ä 10. Modifications of such quadrature formulas have recently been suggested by R. E. Barnhill, J. E. Dennis, Jr. and G. M. Nielson, and by D. Kahaner. We establish here certain empirical observations made by these authors, notably the presence of multiple nodes. We...
متن کاملSimple universal bounds for Chebyshev-type quadratures
A Chebyshev-type quadrature for a probability measure σ is a distribution which is uniform on n points and has the same first k moments as σ. We give bounds for the smallest possible n required to achieve a certain degree k. In contrast to previous results of this type, our bounds use only simple properties of σ and are thus applicable in wide generality. In particular, it is shown that wheneve...
متن کاملRational Szego quadratures associated with Chebyshev weight functions
In this paper we characterize rational Szegő quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szegő quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experime...
متن کاملNonexistence of Chebyshev - Type Quadratures on Infinite Intervals
Quadrature rules on semi-infinite and infinite intervals are considered involving weight functions of the Laguerre and Hermite type. It is shown that such quadrature rules cannot have equal coefficients and real nodes unless the algebraic degree of accuracy is severely limited.
متن کاملContourlet Filter Design Based on Chebyshev Best Uniform Approximation
The contourlet transform can deal effectively with images which have directional information such as contour and texture. In contrast to wavelets for which there exists many good filters, the contourlet filter design for image processing applications is still an ongoing work. Therefore, this paper presents an approach for designing the contourlet filter based on the Chebyshev best uniform appro...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1971
ISSN: 0035-7596
DOI: 10.1216/rmj-1971-1-3-499