共查询到20条相似文献,搜索用时 78 毫秒
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本文给出二阶椭圆型方程的非协调有限元的梯度恢复型后验误差估计.后验误差估计是在Crouzeix-Raviart非协调有限单元上得到的,并且给出误差的上下界,更进一步可以证明所得的后验误差估计在拟一致网格上是渐近精确的,所以误差估计是可行的、有效的.上界证明过程依赖于"Helmholtz分解",下界证明主要依赖"bubble函数".数值结果验证了理论的正确性. 相似文献
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一种有偏估计与最小二乘估计的两种新的相对效率 总被引:1,自引:0,他引:1
考察了线性回归模型的回归系数的一类有偏估计,在均方误差矩阵准则下将其与最小二乘估计(LSE)进行比较,导出了这类有偏估计相对于LSE的两种新的相对效率的上、下界. 相似文献
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本文建立了高阶 Hermite-Fejér 型插值理论,该理论包括收敛准则、误差的下界估计及饱和性等. 相似文献
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本文研究了对称矩阵方程Q+BKS+(BKS)T+BKRKTBT=0近似解的最佳向后误差,得到了向后误差量的上界与下界,并用一个简单的数值例子来说明所得结论. 相似文献
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二次分配问题(Quadratic assignment problem,QAP)属于NP-hard组合优化难题.二次分配问题的线性化及下界计算方法,是求解二次分配问题的重要途径.以Frieze-Yadegar线性化模型和Gilmore-Lawler下界为基础,详细论述了二次分配问题线性化模型的结构特征,并分析了Gilmore-Lawler下界值往往远离目标函数最优值的原因.在此基础上,提出一种基于匈牙利算法的二次分配问题对偶上升下界求解法.通过求解QAPLIB中的部分实例,说明了方法的有效和可行性. 相似文献
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This paper improves error bounds for Gauss, Clenshaw–Curtis and Fejér’s first quadrature by using new error estimates for
polynomial interpolation in Chebyshev points. We also derive convergence rates of Chebyshev interpolation polynomials of the
first and second kind for numerical evaluation of highly oscillatory integrals. Preliminary numerical results show that the
improved error bounds are reasonably sharp. 相似文献
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Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension 总被引:1,自引:0,他引:1
Peter K. Moore 《Numerische Mathematik》2001,90(1):149-177
Summary. I derive a posteriori error estimates for two-point boundary value problems and parabolic equations in one dimension based on interpolation error
estimates. The interpolation error estimates are obtained from an extension of the error formula for the Lagrange interpolating
polynomial in the case of symmetrically-spaced interpolation points. From this formula pointwise and seminorm a priori estimates of the interpolation error are derived. The interpolant in conjunction with the a priori estimates is used to obtain asymptotically exact a posteriori error estimates of the interpolation error. These a posteriori error estimates are extended to linear two-point boundary problems and parabolic equations. Computational results demonstrate
the convergence of a posteriori error estimates and their effectiveness when combined with an hp-adaptive code for solving parabolic systems.
Received April 17, 2000 / Revised version received September 25, 2000 / Published online May 30, 2001 相似文献
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Remarks on a unified theory for classical and generalized interpolation and extrapolation 总被引:1,自引:0,他引:1
Tore Håvie 《BIT Numerical Mathematics》1981,21(4):465-474
A unified theory for generalized interpolation, as developed by Mühlbach, and classical polynomial interpolation is discussed. A fundamental theorem for generalized linear iterative interpolation is given and used to derive generalizations of the classical formulae due to Neville, Aitken and Lagrange. Using Mühlbach's definition of generalized divided differences, Newton's generalized interpolation formula, including an expression for the error term, is derived as a pure identity. 相似文献
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Si-qing Gan Geng SunDepartment of Computer Science Technology Tsinghua University Beijing ChinaAcademy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2002,18(4):629-640
This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable one-leg methods with linear interpolation procedure. 相似文献
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给出了二阶椭圆方程的双线性非协调有限元逼近的梯度恢复后验误差估计.该误差估计是在Q_1非协调元上得到的,并给出了误差的上下界.进一步证明该误差估计在拟一致网格上是渐进精确地.证明依赖于clement插值和Helmholtz分解,数值结果验证了理论的正确性. 相似文献
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MAO Shipeng & SHI Zhongci Institute of Computational Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences PO Box Beijing China 《中国科学A辑(英文版)》2006,49(10)
In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis. 相似文献
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Alejandro Allendes Gilberto Campaa Erwin Hernndez 《Mathematical Methods in the Applied Sciences》2019,42(10):3549-3567
We derive pointwise error estimates for a generalized Oseen when it is approximated by a low order Taylor‐Hood finite element scheme in two dimensions. The analysis is based on estimates for regularized Green's functions associated with a generalized Oseen problem on weighted Sobolev spaces and weighted interpolation results. We apply the maximum norm results to obtain convergence in an optimal control problem governed by a generalized Oseen equation and present a numerical example that allows us to show the behavior of the error. 相似文献
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Francis J. Narcowich Xingping Sun Joseph D. Ward Holger Wendland 《Foundations of Computational Mathematics》2007,7(3):369-390
The purpose of this paper is to get error estimates for spherical basis function (SBF) interpolation and approximation for
target functions in Sobolev spaces less smooth than the SBFs, and to show that the rates achieved are, in a sense, best possible.
In addition, we establish a Bernstein-type theorem, where the smallest separation between data sites plays the role of a Nyquist
frequency. We then use these Berstein-type estimates to derive inverse estimates for interpolation via SBFs. 相似文献
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In this paper, we consider the nonconforming rotated Q 1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis. 相似文献
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In this paper, we consider the nonconforming rotated Q
1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral
meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing
another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic
affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements
whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which
coincides with our theoretical analysis. 相似文献