Results 211 to 220 of about 115,454 (246)

Remainders in Interpolation and Quadrature Formulae

The Mathematical Gazette, 1940
The 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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Gaussian interval quadrature formula

Numerische Mathematik, 2001
Let \(U_N=\{u_0,...,u_N\}, (V_N=\{1,v_1,...,v_N\})\) be a Chebyshev (Markov) system on the interval \([a,b],\) respectively. For a given set of ordered non-overlapping intervals \([c_k,d_k]\subseteq [a,b], k=1,...,n\) the authors consider the multiple node interval quadrature formula (with respect to \(V_N\)) \[ \int_a^b\mu(t)f(t)dt\approx \sum_{k=1}^n\
Borislav Bojanov, Petar Peynov Petrov
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Derivative corrections for quadrature formulas

Advances in Computational Mathematics, 1996
This 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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Ratio asymptotics and quadrature formulas

Constructive Approximation, 1997
Suppose \(p_n\) \((n=0,1,2,\ldots)\) 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 Positive Quadrature Formulas

SIAM Journal on Mathematical Analysis, 1981
We 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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Characterization of Quadrature Formula II

SIAM Journal on Mathematical Analysis, 1984
This 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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Quadrature formulas on combinatorial graphs

International Journal of Wavelets, Multiresolution and Information Processing
The 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, Meyer Z. Pesenson, Hartmut Führ   +2 more
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A quadrature formula for the Hankel transform

Numerical Algorithms, 1995
Quadrature 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

2006
2 (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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Fejér type inequalities for higher order convex functions and quadrature formulae

Aequationes Mathematicae, 2021
Mihaela Ribičić Penava, Josip Pečarić   +1 more
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