Results 231 to 240 of about 21,383 (247)

ON THE ČEBYŠEV QUADRATURE FORMULA

Mathematics of the USSR-Izvestiya, 1969
In this paper we examine several weight functions for which the Cebysev quadrature formula is valid. A method is given in the general case by means of which the degree of precision of the formula may be estimated.
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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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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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On chebyshev quadrature and variance of quadrature formulas

BIT, 1988
The 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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On Quadrature Formulae Near Gaussian Quadrature

1992
In this paper, for product integration on the finite interval [a, b], we consider the class of n-point quadrature formulae Q n of at least algebraic degree 2n – 3. We study a new approach for their characterization using the simple fact that such a quadrature formula is uniquely determined by one node y and its associated weight b. For a given node y ∈
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Minimal Quadrature Formulae as Dual Gauss-Type-Quadratures

1985
Minimal quadrature formulae are considered for the Hilbert space \(H_ 2^ R\) consisting of functions which are analytical on the open disc with radius R and centre at the origin; the inner product is the area integral over the disc. In this paper, such formulae are characterized as dual quadrature formulae of Gaussian type by generalizing Markoff's ...
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Quadrature Formulae

Mathematics of Computation, 1972
J. N. L., A. Ghizzetti, A. Ossicini
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Osculatory Quadrature Formulas

Journal of Mathematics and Physics, 1955
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On Tchebycheff Quadrature Formulas

1988
Let ψ be a bounded nondecreasing function on [a,b] normed by \(\int\limits_a^b {d\psi (x) = 1}\). We say that the distribution dψ admits extended (m, n, dψ) Tchebycheff-quadrature (abbreviated T-q) on [a,b] if there are n nodes zj,n ∈ ℂ, zj,n. real or complex conjugate, such that $$ \int\limits_a^b {f(x)d\psi (x) = \frac{1}{n}\sum\limits_{j = 1}^n {
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