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When the worst case integration error in a family of functions decays
as nfor some > 1 and simple averages along an extensible sequence
match that rate at a set of sample sizes n1 < n2 < < 1...
Symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements
Quadrature Integration Symmetric Triangle
2015/7/3
There have been significant efforts to identify high-order quadrature rules on d-simplex and d-hypercube geometries as evidenced by the surveys in [1–5]. On thed-hypercube, it is well-known that optim...
Quadrature rules and distribution of points on manifolds
Quadrature discrepancy harmonic analysis
2011/2/28
We study the error in quadrature rules on a compact manifold, XN j=1 !jf (zj) − Z
M f(x)dx ≤ cD {zj} V {f} .
Inequalities Between the Quadrature Operators and Error Bounds of Quadrature Rules
Approximate integration Quadrature rules Convex functions of higher order
2008/7/1
The order structure of the set of six operators connected with quadrature rules is established in the class of 3-convex functions. Convex combinations of these operators are studied and their error bo...
On Error Bounds for Gauss-Legendre and Lobatto Quadrature Rules
Convex functions of higher orders Approximate integration Quadrature rules
2008/6/27
The error bounds for Gauss-Legendre and Lobatto quadratures are proved for
four times differentiable functions (instead of six times differentiable functions as in the classical results). Auxiliaril...
On Quadrature Rules, Inequalities and Error Bounds
Approximate integration Quadrature rules Convex functions of higher order
2010/1/22
The order structure of the set of six operators connected with quadrature rules is established in the class of 5-convex functions. An error bound of the Lobatto quadrature rule with five knots is g...