Optimal-by-order Quadrature Formulae for Fast Oscillatory Functions with Inaccurately given a Priori Information
نویسندگان
چکیده
In this article, the authors construct optimal-by-order quadrature formulae for integration of fast oscillatory functions in interpolational classes C 1 The construction of eecient formulae for numerical integration of fast oscillatory functions is based on the application of the residual method and the method of quasi-solutions. Both cases, weak and strong oscillations, are considered. Results of numerical examples are presented. residual method, optimal-by-order quadrature formulae.
منابع مشابه
Optimal-by-accuracy and Optimal-by-order Cubature Formulae in Interpolational Classes
In this paper we constructively solve the problem of optimal integration for fast oscillatory functions of two variables when a priori information is limited. We explore the connection of this problem with the problem of optimal recovery of a function from interpolational classes. optimal-by-order cubature formulae.
متن کاملA Note on Optimal-by-order Cubature Formulae for Fast Oscillatory Functions in Lipschitz Classes
In this article, we consider problems of numerical integration of fast oscillatory functions of two variables when an accurate value of the Lipschitz constant is not available. Using spline approximations, we propose optimal-by-order (with a constant not exceeding two) cubature formulae that are applicable for a wide range of oscillatory patterns.
متن کاملComplex Gaussian quadrature for oscillatory integral transforms
The classical theory of Gaussian quadrature assumes a positive weight function. We will show that in some cases Gaussian rules can be constructed with respect to an oscillatory weight, yielding methods with complex quadrature nodes and positive weights. These rules are well suited for highly oscillatory integrals because they attain optimal asymptotic order. We show that for the Fourier oscilla...
متن کاملA fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations
After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence,...
متن کاملPii: S0898-1221(96)00223-4
Abs t r ac t -An account is given of the role played by moments and modified moments in the construction of quadrature rules, specifically weighted Newton-Cotes and Gaussian rules. Fast and slow Lagrange interpolation algorithms, combined with Gaussian quadrature, as well as linear algebra methods based on moment equations, axe described for generating Newton-Cotes formulae. The weaknesses and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998