Gauss–Turán quadratures of Kronrod type for generalized Chebyshev weight functions
✍ Scribed by Gradimir V. Milovanović; Miodrag M. Spalević
- Publisher
- Springer Milan
- Year
- 2006
- Tongue
- English
- Weight
- 282 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0008-0624
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
As we know, the Chebyshev weight w(x)=(1&x 2 ) &1Â2 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).
In this paper, which is connected with the work of Ma, Rokhlin and Wandzura [1], a numerical scheme for the construction of generalized Gauss-Turin quadrature, replacing the polynomials with functions from a rather wide class, is presented. In a special case, this construction reduces itself to the
Using the theory of s-orthogonality and reinterpreting it in terms of the standard orthogonal polynomials on the real line, we develop a method for constructing Gauss-Turfin-type quadrature formulae. The determination of nodes and weights is very stable. For finding all weights, our method uses an u