Results 191 to 200 of about 67,137 (234)
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Associated symmetric quadrature rules
Applied Numerical Mathematics, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sri Ranga, A. +2 more
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Numerical integration rules near gaussian quadrature
Israel Journal of Mathematics, 1973We call a numerical integration formula based onk nodes which is exact for polynomials of degree at mostn an (n, k) formula. Gaussian quadrature is the unique (2k−1,k) formula. In this paper we give a complete description of all (2k−3,k) formulas, including a characterization of those having all positive weights.
Micchelli, C. A., Rivlin, T. J.
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Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing, 1999The author derives a new class of quadrature rules prescribed for regular and for singular functions as well. The most important property is the fact that the quadrature weights of these rules are positive and the class includes rules of arbitrarily high-order convergence.
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2002
A unified treatment of three point quadrature rules is presented in which the classical rules of mid-point, trapezoidal and Simpson type are recaptured as particular cases. Riemann integrals are approximated for the derivative of the integrand belonging to a variety of norms.
Pietro Cerone, Sever S. Dragomir
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A unified treatment of three point quadrature rules is presented in which the classical rules of mid-point, trapezoidal and Simpson type are recaptured as particular cases. Riemann integrals are approximated for the derivative of the integrand belonging to a variety of norms.
Pietro Cerone, Sever S. Dragomir
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2014
In practice most definite integrals cannot be evaluated exactly. In such cases one must resort to various approximation methods, which can be quite complicated. Any method used to approximate a definite integral is called a quadrature rule. (Quadrature is any process used to construct a square equal in area to that of some given figure.) But in this ...
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In practice most definite integrals cannot be evaluated exactly. In such cases one must resort to various approximation methods, which can be quite complicated. Any method used to approximate a definite integral is called a quadrature rule. (Quadrature is any process used to construct a square equal in area to that of some given figure.) But in this ...
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Stieltjes Polynomials and Related Quadrature Rules
SIAM Review, 1982In this paper we present a survey of theoretical results (some of them new) and numerical evidence of others concerning Stieltjes polynomials, Kronrod schemes and their generalizations applied to integrals with a (classical) nonnegative weight function. The use of these schemes in automatic integration routines is briefly outlined.
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2016
A model is set up which embodies the basic features of Adaptive quadrature routines involving mixed rules. Not before mixed quadrature rules basing on anti-Gaussian quadrature rule have been used for fixing termination criterionin Adaptive quadrature routines.
Singh, Bibhu Prasad, Dash, Rajani Ballav
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A model is set up which embodies the basic features of Adaptive quadrature routines involving mixed rules. Not before mixed quadrature rules basing on anti-Gaussian quadrature rule have been used for fixing termination criterionin Adaptive quadrature routines.
Singh, Bibhu Prasad, Dash, Rajani Ballav
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Blending product-type quadrature rules
BIT, 1982A product type (one dimensional) quadrature rule is one which approximates a finite integral of the integrand function f(x)g(x) by an inner \(f^ TWg\) when f and g are \(m\times 1\) and \(n\times 1\) matrices of function values respectively and W is a \(m\times n\) matrix of weight coefficients.
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1987
Recently Peherstorfer [1] derived a characterization of positive quadrature rules with knots in (a,b). An equivalent characterization will be presented using the positive definiteness of a matrix of moments. This is the one-dimensional case of a characterization of interpolatory cubature formulae, see, for example, [2] and [3].
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Recently Peherstorfer [1] derived a characterization of positive quadrature rules with knots in (a,b). An equivalent characterization will be presented using the positive definiteness of a matrix of moments. This is the one-dimensional case of a characterization of interpolatory cubature formulae, see, for example, [2] and [3].
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Error analysis of quadrature rules
International Journal of Mathematical Education in Science and Technology, 2004Approaches to the determination of the error in numerical quadrature rules are discussed and compared.
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