共查询到20条相似文献,搜索用时 31 毫秒
1.
Tiziano Politi 《BIT Numerical Mathematics》2001,41(4):842-845
In this short paper the formula of the exponential matrix e
A when A is a kew-symmetric real matrix of order 4 is derived. The formula is a generalization of the well known Rodrigues formula for skew-symmetric matrices of order 3.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
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Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A)are bounded in an exponentially decaying manner away from the main diagonal. Bounds obtained by representing the entries of f(A)in terms of Riemann-Stieltjes integrals and by approximating such integrals by Gaussian quadrature rules are also considered. Applications of these bounds to preconditioning are suggested and illustrated by a few numerical examples. 相似文献
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RD-Rational Approximations of the Matrix Exponential 总被引:1,自引:1,他引:0
Restricted Denominator (RD) rational approximations to the matrix exponential operator are constructed by interpolation in points related to Krylov subspaces associated to a rational transform of the particular matrix considered. Convergence analysis are provided. Numerical experiments show the effectiveness of the proposed methods in applications involving discretizations of differential operators. 相似文献
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Jan Johannsen 《Mathematical Logic Quarterly》1998,44(2):205-215
We define a property of substructures of models of arithmetic, that of being length-initial, and show that sharply bounded formulae are absolute between a model and its length-initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing appropriate models as length-initial submodels of some given model. 相似文献
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王金平 《数学物理学报(A辑)》2006,26(1):31-038
该论文主要研究在平面情形下指数型 Radon 变换的连续性,得到了它的近似反演公式,并对近似反演的数值解法加以改进.借助一些技巧,该文从理论上还建立了精确反演公式,从而推广了古典 Radon 变换的相应结果. 相似文献
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设n是大于1的整数,且n=Π_(i=1)tp_itp_i(a_i),令τ_k(a_i),令τ_k((e))(n)=Π_(p_i((e))(n)=Π_(p_i(a_i)||n)d_i(a_i).本文研究了和式D(■)=Σ_(n≤x)d(■)的渐近公式,这里d(■)=∑_(n=ab_1(a_i)||n)d_i(a_i).本文研究了和式D(■)=Σ_(n≤x)d(■)的渐近公式,这里d(■)=∑_(n=ab_12…b_i2…b_i2)1.然后基于以上结论得到了指数除数函数τ_i2)1.然后基于以上结论得到了指数除数函数τ_i((e))(n)的均值的渐近公式,并改进了前人的结果. 相似文献
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由于流体受到某些遗传和不确定信息外力的影响,考虑了含时变时滞随机外力的2D-Navier-Stokes方程.借助随机分析中的It6公式和Burkholder-Davis-Gundy不等式,证明了大粘性系数情形方程整体弱解的均方指数稳定和几乎必然指数稳定. 相似文献
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Stefan Glasauer 《Geometriae Dedicata》1997,68(1):101-121
We establish extensions of the Crofton formula and, under some restrictions, of the principal kinematic formula of integral geometry from curvature measures to generalized curvature measures of convex bodies. We also treat versions for finite unions of convex bodies. As a consequence, we get a new intuitive interpretation of the area measures of Aleksandrov and Fenchel–Jessen. 相似文献
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We propose a new measure of conditioning for the exponential of a block triangular matrix. We also show that different condition numbers must be used to assess the accuracy of different algorithms which implement diagonal Padé with scaling and squaring. 相似文献
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本文利用三角和等式以及既约剩余系的性质, 研究了广义三项指数和的四次均值的计算问题, 并给出了特定情形下的一些等式. 相似文献
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In this paper, the authors use the analytic methods and the properties of
character sums mod p to study the computational problem of one kind of mean value
involving the classical Dedekind sums and two-term exponential sums, and give an exact
computational formula for it. 相似文献
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We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying +∞ ∞ |f(t)| p e -α(t) dt) 1/p ,1 p ∞,and α(t) is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new. 相似文献
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This paper proposes an accurate dense output formula for exponential integrators. The computation of matrix exponential function is a vital step in implementing exponential integrators. By scrutinizing the computational process of matrix exponentials using the scaling and squaring method, valuable intermediate results in this process are identified and then used to establish a dense output formula. Efficient computation of dense outputs by the proposed formula enables time integration methods to set their simulation step sizes more flexibly. The efficacy of the proposed formula is verified through numerical examples from the power engineering field. 相似文献
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Some well-known L-type formulae, i.e., L1, L1-2, and L1-2-3 formulae,
are usually employed to approximate the Caputo fractional derivative of order α ∈
(0, 1). In this paper, we aim to elaborate on the stability and convergence analyses
of some finite difference methods (FDMs) for solving the subdiffusion equation, i.e.,
a diffusion equation which exploits the Caputo time-fractional derivative of order $α$.
In fact, the FDMs considered here are based on the usual central difference scheme
for the spatial derivative, and the Caputo derivative is approximated by using methods such as the L1, L1-2, and L1-2-3 formulae. Thanks to a specific type of the
discrete version of the Gronwall inequality, we show that the FDMs are unconditionally stable in the maximum norm and also discrete $H^1$ norm. Then, we prove that
the finite difference method which uses the L1, L1-2, and L1-2-3 formulae has the
global order of convergence $2−α$, $3−α$, and 3, respectively. Finally, some numerical
tests confirm the theoretical results. A brief conclusion finishes the paper. 相似文献
17.
In this paper we consider the asymptotic behaviour of the error term Q(x;h/q), which is defined by (1.2). In particular, we derive a certain lower bound estimate of this function when h, k and q are fixed integers, and study the non-trivial upper bound estimates of the mean value of Q(x;h/q). 相似文献
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给出了线性分段连续型随机微分方程指数Euler方法的均方指数稳定性.经典的对稳定性理论分析,通常应用的是Lyapunov泛函理论,然而,应用该方程本身的特点和矩阵范数的定义给出了该方程精确解的均方稳定性.以往对于该方程应用隐式Euler方法得到对于任意步长数值解的均方稳定性,而应用显式Euler方法得到了相同的结果.最... 相似文献
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This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall's integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations. 相似文献
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