共查询到20条相似文献,搜索用时 62 毫秒
1.
《Journal of Computational and Applied Mathematics》2001,127(1-2):153-171
Gaussian formulas are among the most often used quadrature formulas in practice. In this survey, an overview is given on stopping functionals for Gaussian formulas which are of the same type as quadrature formulas, i.e., linear combinations of function evaluations. In particular, methods based on extended formulas like the important Gauss–Kronrod and Patterson schemes, and methods which are based on Gaussian nodes, are presented and compared. 相似文献
2.
Ken’ichiro Tanaka Masaaki Sugihara Kazuo Murota Masatake Mori 《Numerische Mathematik》2009,111(4):631-655
The double exponential (DE) formulas for numerical integration are known to be highly efficient, more efficient than the single
exponential (SE) formulas in many cases. Function classes suited to the SE formulas have already been investigated in the
literature through rigorous mathematical analysis, whereas this is not the case with the DE formulas. This paper identifies
function classes suited to the DE formulas in a way compatible with the existing theoretical results for the SE formulas.
The DE formulas are good for more restricted classes of functions, but more efficient for such functions. Two concrete examples
demonstrate the subtlety in the behavior of the DE formulas that is revealed by our theoretical analysis. 相似文献
3.
C. Krattenthaler 《Israel Journal of Mathematics》1995,90(1-3):67-79
New bideterminantal formulas for the irreducible symplectic and orthogonal characters are given that generalize the classical
bideterminantal formulas. These formulas are analogous to Regev’s (Israel J. Math. 80 (1992), 155–160) bideterminantal formulas
for Schur functions, the irreducible general linear characters. Also, new bideterminantal formulas for Proctor’s intermediate
symplectic characters are derived. 相似文献
4.
《Journal of Computational and Applied Mathematics》2001,135(2):313-324
We derive scalar boundary integral equation formulas for both interior and exterior biharmonic equations with the Dirichlet boundary data. They are based on indirect boundary integral equation formulas, so-called the Chakrabarty and Almansi formulas. The scalar formulas are derived through an unconventional variational approach. The unique solvability results of the formulas are also obtained. 相似文献
5.
A. I. Zadorin 《Computational Mathematics and Mathematical Physics》2013,53(12):1808-1818
Cubature formulas for evaluating the double integral of a two-variable function with boundary-layer components are constructed and studied. Because of the boundary-layer components, the cubature formulas based on Newton-Cotes formulas become considerably less accurate. Analogues of the trapezoidal and Simpson rules that are exact for the boundary-layer components are constructed. Error estimates for the constructed formulas are derived that are uniform in the gradients of the integrand in the boundary layers. 相似文献
6.
《Journal of Complexity》1999,15(3):299-316
Lower bounds for the error of quadrature formulas with positive weights are proved. We get intractability results for quasi-Monte Carlo methods and, more generally, for positive formulas. We consider general classes of functions but concentrate on lower bounds for relatively small classes of trigonometric polynomials. We also conjecture that similar lower bounds hold for arbitrary quadrature formulas and state different equivalent conjectures concerning positive definiteness of certain matrices and certain extremal problems for trigonometric polynomials. We also study classes of functions with weighted norms where some variables are “more important” than others. Positive quadrature formulas are then tractable iff the sum of the weights is bounded. 相似文献
7.
Youjian Shen 《高等学校计算数学学报(英文版)》2006,15(1):50-59
In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x)so that the Gaussian quadrature formulas have degree n-1.The error estimates of the formulas are obtained.It is found from the numerical examples that the convergence rate and the accu- racy of the approximation results are satisfactory.Moreover,the rate and the accuracy can be improved by choosing appropriate weight functions. 相似文献
8.
Muniru Aderemi Asiru 《International Journal of Mathematical Education in Science & Technology》2013,44(6):911-923
In this note, we provide basic asymptotic formulas for approximating large g-gonal sequence factorials by using Stirling and Burnside asymptotic approximation formulas for large factorials. More accurate asymptotic approximation formulas for large g-gonal sequence factorials resulting from some recent, more accurate asymptotic formulas for large factorials that have appeared in the literature are presented. 相似文献
9.
George K. Yang 《Applicable analysis》2013,92(5):501-507
We investigate the wavelet transforms of tempered distributions in a way that closely links their Fourier transforms and wavelet transforms. Two exchange formulas of the convolution and the multiplication of wavelet transforms of tempered distributions are established. We call these formulas the quasi-exchange formulas for wavelet transforms of distributions, because of the resemblance between these formulas and the well-known exchange formula for Fourier transforms. 相似文献
10.
The cubature formulas we consider are exact for spaces of Haar polynomials in one or two variables. Among all cubature formulas, being exact for the same class of Haar polynomials, those with a minimal number of nodes are of special interest. We outline here the research and construction of such cubature formulas. 相似文献
11.
Daniel A. Klain 《Annals of Combinatorics》1997,1(1):353-366
In analogy to valuation characterizations and kinematic formulas of convex geometry, we develop a combinatorial theory of invariant valuations and kinematic formulas for finite lattices. Combinatorial kinematic formulas are shown to have application to some probabilistic questions, leading in turn to polynomial identities for Möbius functions and Whitney numbers. 相似文献
12.
We define quadrature formulas for integrals with weight functionsby applying a given approximation method locally. This allowsthe generalisation of different quadrature formulas, e.g., thecompound Newton-Cotes formulas, Gauss summation formulas, orGregory's formulas, to the case of weighted integrals, as wellas to construct new quadrature formulas, and to derive errorestimates for all these quadrature formulas. The estimates consideredhere are mainly of the form |R[f]|c||f(r)||, provided the underlyingapproximation method is exact for polynomials of degree <r(R[f] is the quadrature error). Explicit, asymptotically sharperror estimates are obtained for arbitrary integrable weightfunctions. Further, estimates are obtained for the case thatthe quadrature error is of higher order than the approximationerror. 相似文献
13.
数值积分公式中间点的渐近性质及其应用 总被引:17,自引:1,他引:16
主要研究了三类数值积分公式的中间点的渐近性质,得到了更一般性的结果.基于中间点的渐近性质,获得了数值积分的校正公式及其条件误差估计.数值例子显示了校正公式的精度明显高于对应的计算公式. 相似文献
14.
A. V. Voznyuk 《Journal of Mathematical Sciences》1993,66(2):2139-2143
Expansions in the elgenfunctions of the Sturm-Liouville problem and perturbation expansions are applied to obtain asymptotic formulas for parabolic cylindrical functions and Hermite polynomials for large n. The formulas are compared with previously published formulas and, in particular, a numerical comparison is made for one Hermite polynomial.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 19–24, 1987. 相似文献
15.
《随机分析与应用》2013,31(6):1553-1576
Abstract Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for both, Itô and Stratonovich stochastic differential equation systems with multi-dimensional Wiener processes. Due to the very complex formulas arising for higher order expansions, an advantageous graphical representation by coloured trees is developed. The convergence of truncated formulas is analyzed and estimates for the truncation error are calculated. Finally, the stochastic Taylor formulas based on coloured trees turn out to be a generalization of the deterministic Taylor formulas using plain trees as recommended by Butcher for the solutions of ordinary differential equations. 相似文献
16.
考虑对具有有界混合差分的二元光滑函数类B^γ,p,θ的求积公式,本文证明了Fibonacci求积公式是渐近最优的,并求出了春误差的渐近最优价。 相似文献
17.
Beda Chan 《Insurance: Mathematics and Economics》1982,1(4):241-243
We apply power series techniques for differential equations on probability generating functions to derive recursive formulas for discrete compound distributions. Such formulas are computationally effective and useful in risk theory. 相似文献
18.
In this paper, we present recursive formulas for the sequential determination of the generalized LM-inverse of a general matrix. The formulas are developed for a matrix augmented by a column. These formulas are particularized to obtain also recursive relations for the generalized L-inverse of a general matrix augmented by a column. 相似文献
19.
《Journal of Computational and Applied Mathematics》1998,89(2):263-274
A plane elasticity problem leads us to a biharmonic equation with the boundary condition, consisting of first order partial derivatives. We apply the boundary integral equation formulas by Y. Jeon (1996) for the problem. Derivation of the formulas and the concerned analysis and numerical examples are presented. The formulas are especially efficient in evaluating the stress tensor on the boundary as well as inside the domain. It is the stress tensor components that are physically important quantities for the problem. 相似文献
20.
R. Wong 《Numerische Mathematik》1982,39(3):351-360
Summary Quadrature formulas are obtained for the Fourier and Bessel transforms which correspond to the well-known Gauss-Laguerre formula for the Laplace transform. These formulas provide effective asymptotic approximations, complete with error bounds. Comparison is also made between the quadrature formulas and the asymptotic expansions of these transforms.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada under Contract A7359 相似文献