Results 181 to 190 of about 1,199 (217)
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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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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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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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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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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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Quadrature formulas on combinatorial graphs
International Journal of Wavelets, Multiresolution and Information ProcessingThe goal of the paper is to establish quadrature formulas on combinatorial graphs. Three types of quadrature formulas are developed. Quadrature formulas of the first type are obtained through interpolation by variational splines. This set of formulas is exact on spaces of variational splines on graphs.
Isaac Z. Pesenson +2 more
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A quadrature formula for the Hankel transform
Numerical Algorithms, 1995Quadrature formulas for the integral transform to be composed by two Hankel transforms and for the closely related Hankel transform are presented, the error produced by this algorithm for a class of piecewise continuous functions is estimated and some numerical examples are listed.
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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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