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SzegőLobatto quadrature rules
"... Gausstype quadrature rules with one or two prescribed nodes are well known and are commonly referred to as GaussRadau and GaussLobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szegő quadrature rules are analogs of Gauss quadrature rules for the int ..."
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Gausstype quadrature rules with one or two prescribed nodes are well known and are commonly referred to as GaussRadau and GaussLobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szegő quadrature rules are analogs of Gauss quadrature rules
AntiSzegő quadrature rules
, 2006
"... Szegő quadrature rules are discretization methods for approximating integrals of the form ∫ π −π f(e^it)dµ(t). This paper presents a new class of discretization methods, which we refer to as antiSzegő quadrature rules. AntiSzegő rules can be used to estimate the error in Szegő quadrature rules: u ..."
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Cited by 2 (0 self)
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Szegő quadrature rules are discretization methods for approximating integrals of the form ∫ π −π f(e^it)dµ(t). This paper presents a new class of discretization methods, which we refer to as antiSzegő quadrature rules. AntiSzegő rules can be used to estimate the error in Szegő quadrature rules
ON APPELTYPE QUADRATURE RULES
"... Abstract. The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler–MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) ..."
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Abstract. The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler–MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd
On the variance of the Gaussian quadrature rule
, 1997
"... Denote by P n =1 a f (x ) the Gaussian quadrature rule for the integral R 1 \Gamma1 f (x) dx. We give a simple explicit expression for the "variance" P n =1 a 2 . The method can be used to obtain similar results for the Lobatto rule. ..."
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Denote by P n =1 a f (x ) the Gaussian quadrature rule for the integral R 1 \Gamma1 f (x) dx. We give a simple explicit expression for the "variance" P n =1 a 2 . The method can be used to obtain similar results for the Lobatto rule.
Hybrid GaussTrapezoidal Quadrature Rules
 SIAM Journal on Scientific Computing
, 1999
"... . A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily highorder convergence. The quadratures result from alterations to the trapezoidal r ..."
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Cited by 55 (1 self)
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. A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily highorder convergence. The quadratures result from alterations to the trapezoidal
Nested Families of Quadrature Rules
, 2010
"... I am involved in a software project developing sparse grid codes which allow the user to choose, for each spatial component, the quadrature family, rate of growth, and anisotropy weight. The software library is called SGMGA: ..."
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I am involved in a software project developing sparse grid codes which allow the user to choose, for each spatial component, the quadrature family, rate of growth, and anisotropy weight. The software library is called SGMGA:
Calculation of Gauss–Kronrod Quadrature Rules
 Mathematics of Computation
, 1997
"... Abstract. The Jacobi matrix of the (2n+1)point GaussKronrod quadrature rule for a given measure is calculated efficiently by a fiveterm recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the JacobiKronrod matrix analytically. The nodes and ..."
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Cited by 19 (0 self)
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Abstract. The Jacobi matrix of the (2n+1)point GaussKronrod quadrature rule for a given measure is calculated efficiently by a fiveterm recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the JacobiKronrod matrix analytically. The nodes
Computing Discrepancies of Smolyak Quadrature Rules
 J. COMPLEXITY
, 1996
"... In recent years, Smolyak quadrature rules (also called quadratures on hyperbolic cross points or sparse grids) have gained interest as a possible competitor to number theoretic quadratures for high dimensional problems. A standard way of comparing the quality of multivariate quadrature formulas cons ..."
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Cited by 14 (1 self)
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In recent years, Smolyak quadrature rules (also called quadratures on hyperbolic cross points or sparse grids) have gained interest as a possible competitor to number theoretic quadratures for high dimensional problems. A standard way of comparing the quality of multivariate quadrature formulas
COMPUTATION OF GAUSSKRONROD QUADRATURE RULES
"... Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)point GaussKronrod 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 GaussKronrod 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
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