Results 181 to 190 of about 4,085 (219)
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On chebyshev quadrature and variance of quadrature formulas
BIT, 1988The purpose of this note is to give an example which demonstrates that one can achieve much higher algebraic precision with a quadrature rule with small but not minimal variance than with a Chebyshev rule with minimal variance.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1950
1. It is frequently required to find the numerical value of the definite integralIt is, however, often found that even if the analytical expression off(x) is given, it cannot be integrated in terms of known elementary functions. The elliptic integrals are perhaps the best known examples of functions of this type; and more common are cases wheref(x) is ...
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1. It is frequently required to find the numerical value of the definite integralIt is, however, often found that even if the analytical expression off(x) is given, it cannot be integrated in terms of known elementary functions. The elliptic integrals are perhaps the best known examples of functions of this type; and more common are cases wheref(x) is ...
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Derivative corrections for quadrature formulas
Advances in Computational Mathematics, 1996This paper is concerned with the construction of quadrature rules that include approximations to derivative correction terms for standard formulas. The correction terms require only the use of the integrand values from the original formula. This is a standard method for improving simple quadrature formulas.
William F. Ford, Yuesheng Xu, Yunhe Zhao
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Remainders in Interpolation and Quadrature Formulae
The Mathematical Gazette, 1940The determination of the errors involved in interpolation or quadrature formulae often involves complicated reasoning. There are many cases, however, where the remainder can be obtained very easily. These cases belong to the class which we call simplex. In general a formula will be expressible in the form
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Latin rectangles and quadrature formulas
European Journal of Combinatorics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nikolai M. Dobrovol'skii +3 more
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RATIONAL FUNCTIONS AND QUADRATURE FORMULAE
Analysis, 1988Summary: In the theory of classical, strong and trigonometric moment problems quadrature formulae for the linear functional, defined by the moments, can be obtained by using ordinary or modified approximants of certain continued fractions as intermediaries.
Njåstad, Olav, Thron, W. J.
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Ratio asymptotics and quadrature formulas
Constructive Approximation, 1997Suppose \(p_n\) \((n=0,1,2,\ldots)\) is a sequence of orthogonal polynomials on the real line, satisfying a three-term recurrence relation \(tp_n(t) = a_{n+1}p_{n+1}(t)+b_np_n(t)+a_np_{n-1}(t)\). The author gives a method for obtaining the asymptotic behaviour of the ratio \(s_n(z)/p_n(z)\) for a comparison sequence \(s_n\) \((n=0,1,2,\ldots)\) of ...
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Characterization of Quadrature Formula II
SIAM Journal on Mathematical Analysis, 1984This paper is concerned with interpolatory quadrature formulas of the type \[ (1)\quad \int^{+1}_{- 1}f(x)w(x)dx=\sum^{n}_{i=1}\lambda_ i\quad f(x_ i)+R_ n(f) \] where ...
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Characterization of Positive Quadrature Formulas
SIAM Journal on Mathematical Analysis, 1981We give a complete description of those numerical integration formulas based on n nodes which have positive weights and are exact for polynomials of degree equal or less than $2n - 1 - m$, where $0 \leqq m \leqq n$.
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The Coefficients of Optimal Quadrature Formulas
20062 (R) are studied by means of a variational method. Here w(x) is a weight function, χΩ(x) is the characteristic function of the interval Ω, and c(β) are the coefficients of the quadrature formula. The results generalize some results by A. Sard, L. F. Meyers, I. J. Schoenberg, S. D. Silliman (1-4), and others derived by the method of splines.
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