共查询到20条相似文献,搜索用时 46 毫秒
1.
A new iterative method is proposed for computing partial derivatives of many eigenpairs. This method simultaneously computes a few eigenpair partial derivatives. For each origin shift, partial derivatives of eigenpairs whose eigenvalues are closest to the origin shift can be computed. Hence, this method may be used for partial derivatives of all eigenpairs. Convergence of the proposed method is established. Finally numerical experiments are given to show the effectiveness of the proposed method. 相似文献
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We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.) 相似文献
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The Fractional Derivatives of a Fractal Function 总被引:2,自引:0,他引:2
Kui YAO Wei Yi SU Song Ping ZHOU 《数学学报(英文版)》2006,22(3):719-722
The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function. 相似文献
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Feilong Cao 《Journal of Approximation Theory》2005,132(2):241-257
We characterize the directional derivatives of multidimensional Bernstein operators by a new measure of smoothness. This task is carried out by means of establishing the relation between the asymptotic behavior of the derivatives and the smoothness of the functions they approximate. The obtained results generalize the corresponding ones for univariate Bernstein operators. 相似文献
6.
Mirjana Stojanovi 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5458-5475
We give an extension of Colombeau algebra of generalized functions to fractional derivatives. We apply it in solving ODEs and PDEs with entire and fractional derivatives with respect to temporal and spatial variables. We give applications to ODEs and PDEs driven by fractional derivatives of delta distribution. 相似文献
7.
E. A. Volkov 《Computational Mathematics and Mathematical Physics》2007,47(4):638-643
A combined grid method for solving the Dirichlet problem for the Laplace equation in a rectangular parallelepiped is proposed. At the grid points that are at the distance equal to the grid size from the boundary, the 6-point averaging operator is used. At the other grid points, the 26-point averaging operator is used. It is assumed that the boundary values have the third derivatives satisfying the Lipschitz condition on the faces; on the edges, they are continuous and their second derivatives satisfy the compatibility condition implied by the Laplace equation. The uniform convergence of the grid solution with the fourth order with respect to the grid size is proved 相似文献
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一组三个函数乘积的高阶导数公式及其行列式表示 总被引:2,自引:0,他引:2
谭福锦 《数学的实践与认识》2006,36(7):372-378
研究了三个函数乘积的高阶导数,得到了一组相应的导数公式.利用这些公式求该类函数的高阶导数以及进行近似计算,或做函数的近似表示,将起到较好的简化作用. 相似文献
9.
《Stochastic Processes and their Applications》2020,130(8):4808-4858
In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter first-order derivatives, the parameter can be estimated online. To analyze the asymptotic behavior of such methods, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. These properties are studied here. Under regularity conditions, we show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the same derivatives are geometrically ergodic. 相似文献
10.
In this paper,some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωr(4)λ(f,t)w(4)s(O≤λ≤1)are given.The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated. 相似文献
11.
本文研究了有界解析函数的n阶导数估计.利用有界解析函数泰勒展开式的系数估计,得到了n阶导数估计的一般式,改进了已有的相关结果. 相似文献
12.
Jian Yuan Song Gao Guozhong Xiu Bao Shi 《Journal of Applied Analysis & Computation》2020,10(5):2008-2023
Initialization of fractional differential equations remains an ongoing problem. The initialization function approach and the infinite state approach provide two effective ways of dealing with this issue. The purpose of this paper is to prove the equivalence of the initialized Riemann-Liouville derivative and the initialized Caputo derivative with arbitrary order. By synthesizing the above two initialization theories, diffusive representations of the two initialized derivatives with arbitrary order are derived. The Laplace transforms of the two initialized derivatives are shown to be identical. Therefore, the two most commonly used derivatives are proved to be equivalent as long as initial conditions are properly imposed. 相似文献
13.
关于Bernstein型多项式导数的特征 总被引:5,自引:1,他引:4
利用高阶光滑模研究Bernstein型多项式的高阶导数问题,用函数的光滑性刻画Bernstein型多项式的高阶导数的特征,得到了一个等价定理。 相似文献
14.
孙桂荣 《纯粹数学与应用数学》2011,27(3):348-356
运用值分布理论研究了高阶慢增长系数线性微分方程的解及其导数的不动点问题.当存在某个系数对方程的解的性质起主要支配作用时,得到了方程解及其导数的不动点收敛指数的精确估计,推广了有关文献中的结论. 相似文献
15.
Rajesh Pereira 《Journal of Mathematical Analysis and Applications》2005,306(2):425-431
We prove that a majorization-type relation among the root sets of three polynomials implies that the same relation holds for the root sets of their derivatives. We then use this result to give a unified derivation of the classical results due to Sz.-Nagy, Robinson, Meir and Sharma which relate the span of a polynomial to the spans of its first or higher derivatives. We also show how this relation can be generated by interlacing polynomials. 相似文献
16.
L. Y. Zhu & L. Qiu 《分析论及其应用》2012,28(2):135-145
In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn (f, qn ; x) approximating to f ′ (x) asn →∞, which is a generalization of that relating the classical case qn = 1. On the other hand, we study the convergence properties of derivatives of the limit q-Bernstein operators B ∞ (f, q; x) as q → 1- . 相似文献
17.
Vladimir Kozlov 《偏微分方程通讯》2013,38(1):24-51
We consider the Dirichlet problem for strongly elliptic systems of order 2m in convex domains. Under a positivity assumption on the Poisson kernel it is proved that the weak solution has bounded derivatives up to order m provided the outward unit normal has no big jumps on the boundary. In the case of second order symmetric systems in plane convex domains the boundedness of the first derivatives is proved without the assumption on the normal. 相似文献
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本文利用加权Ditzian-Totik光滑模证明Bernstein型算子的线性组合加权逼近阶估计和等价定理;同时,研究加Jacobi权下Benstein型算子的高阶导数与所逼近函数光滑性之间的关系. 相似文献
20.
We introduce a new class of smooth pseudodifferential operators on the torus whose calculus allows us to show that global hypoellipticity with a finite loss of derivatives of certain systems of pseudodifferential operators is stable under perturbations by lower order systems of pseudodifferential operators whose order depends on the loss of derivatives. We also present some applications. 相似文献