SIAM Journal on Numerical Analysis
Anti-Gaussian quadrature formulas
Mathematics of Computation
The remainder term for analytic functions of symmetric Gaussian quadratures
Mathematics of Computation
On stratified extensions of Gauss-Laguerre and Gauss-Hermite quadrature formulas
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Modified anti-Gauss and degree optimal average formulas for Gegenbauer measure
Applied Numerical Mathematics
Error bounds of certain Gaussian quadrature formulae
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the interval [-1,1]. The kernel of the remainder term in anti-Gaussian quadrature formulae is analyzed. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L^~-error bounds of anti-Gauss quadratures. Moreover, the effective L^1-error estimates are also derived. The results obtained here are an analogue of some results of Gautschi and Varga (1983) [11], Gautschi et al. (1990) [9] and Hunter (1995) [10] concerning Gaussian quadratures.