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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
Symmetric GaussLobatto And Modified AntiGauss Rules
, 2002
"... The present paper is concerned with symmetric GaussLobatto quadrature rules, i.e., with GaussLobatto rules associated with a nonnegative symmetric measure on the real axis. We propose a modi cation of the antiGauss quadrature rules recently introduced by Laurie, and show that the symmetric Gauss ..."
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The present paper is concerned with symmetric GaussLobatto quadrature rules, i.e., with GaussLobatto rules associated with a nonnegative symmetric measure on the real axis. We propose a modi cation of the antiGauss quadrature rules recently introduced by Laurie, and show that the symmetric GaussLobatto
On GaussLobatto integration on the triangle
 SIAM J. Numer. Anal
"... Abstract. A recent result in [2] on the nonexistence of GaussLobatto cubature rules on the triangle is strengthened by establishing a lower bound for the number of nodes of such rules. A method of constructing Lobatto type cubature rules on the triangle is given and used to construct several exam ..."
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Abstract. A recent result in [2] on the nonexistence of GaussLobatto cubature rules on the triangle is strengthened by establishing a lower bound for the number of nodes of such rules. A method of constructing Lobatto type cubature rules on the triangle is given and used to construct several
On error bounds for Gauss–Legendre and Lobatto quadrature rules
 J. Ineq. Pure & Appl. Math
, 2006
"... ABSTRACT. 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). Auxiliarily we establish some inequalities for 3–convex functions. ..."
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ABSTRACT. 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). Auxiliarily we establish some inequalities for 3–convex functions.
ON ERROR BOUNDS FOR GAUSS–LEGENDRE AND LOBATTO QUADRATURE RULES
 JOURNAL OF INEQUALITIES IN PURE AND APPLIED MATHEMATICS
, 2006
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Highorder GaussLobatto formulae
"... Currently, the method of choice for computing the (n + 2)point GaussLobatto quadrature rule for any measure of integration is to first generate the Jacobi matrix of order n + 2 for the measure at hand, then modify the three elements at the right lower corner of the matrix in a manner proposed in 1 ..."
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Cited by 2 (0 self)
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Currently, the method of choice for computing the (n + 2)point GaussLobatto quadrature rule for any measure of integration is to first generate the Jacobi matrix of order n + 2 for the measure at hand, then modify the three elements at the right lower corner of the matrix in a manner proposed
Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa
 Calcolo
"... Telephone and fax numbers: Tel (222) 2295637, Fax 2295636. Abstract For a given θ ∈ (a, b), we investigate the question whether there exists a positive quadrature formula with maximal degree of precision which has the prescribed abscissa θ plus possibly a and/or b, the endpoints of the interval of ..."
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Telephone and fax numbers: Tel (222) 2295637, Fax 2295636. Abstract For a given θ ∈ (a, b), we investigate the question whether there exists a positive quadrature formula with maximal degree of precision which has the prescribed abscissa θ plus possibly a and/or b, the endpoints of the interval of integration. This study relies on recent results on the location of roots of quasiorthogonal polynomials. The above positive quadrature formulae are useful in studying problems in onesided polynomial L1 approximation.
Computation of rational SzegőLobatto quadrature formulas
, 2009
"... Szego ̋ quadrature formulas are analogs of Gauss quadrature rules when dealing with the approximate integration of periodic functions, since they exactly integrate trigonometric polynomials of as high degree as possible, or more generally Laurent polynomials which can be viewed as rational functions ..."
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Szego ̋ quadrature formulas are analogs of Gauss quadrature rules when dealing with the approximate integration of periodic functions, since they exactly integrate trigonometric polynomials of as high degree as possible, or more generally Laurent polynomials which can be viewed as rational
Computation of rational SzegőLobatto quadrature formulas
"... Szego ̋ quadrature formulas are analogs of Gauss quadrature rules when dealing with the approximate integration of periodic functions, since they exactly integrate trigonometric polynomials of as high degree as possible, or more generally Laurent polynomials which can be viewed as rational function ..."
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Szego ̋ quadrature formulas are analogs of Gauss quadrature rules when dealing with the approximate integration of periodic functions, since they exactly integrate trigonometric polynomials of as high degree as possible, or more generally Laurent polynomials which can be viewed as rational
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.
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