Chebyshev quadrature rules for a new class of weight functions

Autor:	Lawrence Stalla, Paul F. Byrd
Rok vydání:	1984
Předmět:	Discrete mathematics Computational Mathematics Algebra and Number Theory Applied Mathematics Chebyshev filter Gauss–Kronrod quadrature formula Decimal Mathematics Clenshaw–Curtis quadrature Quadrature (mathematics)
Zdroj:	Mathematics of Computation. 42:173-181
ISSN:	1088-6842 0025-5718
DOI:	10.1090/s0025-5718-1984-0725992-1
Popis:	Proof is given that the weight functions w ( x , p ) = 1 / [ π ( p + x ) x ( 1 − x ) ] w(x,p) = 1/[\pi (p + x)\sqrt {x(1 - x)} ] on (0, 1) admit Chebyshev quadratures for any fixed p ⩾ 1 p \geqslant 1 , and every N. For the particular cases when p = 1 p = 1 and p = 2 p = 2 , the nodes are tabulated to ten decimal places for N-point rules with N = 2 , 4 , 6 , 8 N = 2,4,6,8 , and 12. Numerical tables are also given for a coefficient in the expression of the error term.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d40d68e2e56ce0c8ed2868997115d113 https://doi.org/10.1090/s0025-5718-1984-0725992-1 Zobrazit plný text záznamu