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Results 11 - 20
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629
COMPUTATION OF GAUSS-KRONROD QUADRATURE RULES
"... Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n + 1 from certain mixed moments, and then computes a partial spectral ..."
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Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n + 1 from certain mixed moments, and then computes a partial
Obtaining ... Convergence for Lattice Quadrature Rules
"... Good lattice quadrature rules are known to have O(N -2+# ) convergence for periodic integrands with sufficient smoothness. Here it is shown that applying the baker's transformation to lattice rules gives O(N -2+# ) convergence for nonperiodic integrands with sufficient smoothness. This appro ..."
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Good lattice quadrature rules are known to have O(N -2+# ) convergence for periodic integrands with sufficient smoothness. Here it is shown that applying the baker's transformation to lattice rules gives O(N -2+# ) convergence for nonperiodic integrands with sufficient smoothness
Gauss-type quadrature rules for rational functions
- in Numerical Integration IV
"... Abstract. When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as ..."
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Cited by 13 (4 self)
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Abstract. When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so
Generalized Gaussian Quadrature Rules on Arbitrary Polygons
, 2009
"... In this paper, we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons. These quadratures have desirable properties such as positivity of weights and interiority of nodes ..."
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Cited by 22 (3 self)
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In this paper, we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons. These quadratures have desirable properties such as positivity of weights and interiority of nodes
NEW QUADRATURE RULES FOR BERNSTEIN MEASURES ON THE INTERVAL
"... Abstract. In the present paper, we obtain quadrature rules for Bernstein measures on, having a fixed number of nodes and weights such that they exactly integrate functions in the linear space of polynomials with real coefficients. ..."
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Abstract. In the present paper, we obtain quadrature rules for Bernstein measures on, having a fixed number of nodes and weights such that they exactly integrate functions in the linear space of polynomials with real coefficients.
A constraint on extensible quadrature rules
"... Abstract When the worst case integration error in a family of functions decays as n −α for some α > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 < · · · < ∞, then these sample sizes must grow at least geometrically. More precisely, ..."
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, n k+1 /n k ≥ ρ must hold for a value 1 < ρ < 2 that increases with α. This result always rules out arithmetic sequences but never rules out sample size doubling. The same constraint holds in a root mean square setting.
Results 11 - 20
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629
