منابع مشابه
Gaussian quadratures for oscillatory integrands
We consider a Gaussian type quadrature rule for some classes of integrands involving highly oscillatory functions of the form f (x) = f 1 (x) sin ζ x + f 2 (x) cos ζ x, where f 1 (x) and f 2 (x) are smooth, ζ ∈ R. We find weights σ ν and nodes x ν , ν = 1, 2,. .. , n, in a quadrature formula of the form 1 −1 f (x) dx ≈ n ν=1 σ ν f (x ν) such that it is exact for all polynomials f 1 (x) and f 2 ...
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them particularly important in solvinG physical problems. Also, Gaussian integration provides a highly accurate and efficient algorithm for integrating functions. The value of the methods I describe in this installment of “Computing Prescriptions” depends on the basic assumption that a finite-order polynomial can effectively approximate a function. Therefore, a finite sum of orthogonal polynomi...
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In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi,...
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Given a weight function a>(x) on (a, ß), and a system of polynomials {p*(x)}"=oi with degree pk{x) = k, we consider the problem of constructing Gaussian quadrature rules fff(x)w(x)dx = Yf= i V/ift"') from "modified moments" vk = ^pk(x)w(x)dx. Classical procedures take pk{x) = xk, but suffer from progressive ill-conditioning as n increases. A more recent procedure, due to Sack and Donovan, takes...
متن کاملOn Generalized Gaussian Quadratures for Bandlimited Exponentials
We review the methods in [4] and [24] for constructing quadratures for bandlimited exponentials and introduce a new algorithm for the same purpose. As in [4], our approach also yields generalized Gaussian quadratures for exponentials integrated against a non-sign-definite weight function. In addition, we compute quadrature weights via l and l∞ minimization and compare the corresponding quadratu...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1974
ISSN: 0035-7596
DOI: 10.1216/rmj-1974-4-2-287