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本文首先将证明矩形剖分单元上的Lobatto点,Gauss点和拟Lobatto点分别是二维投影型插值算子函数,梯度和二阶导数的逼近佳点;然后考虑了二阶椭圆边值问题的有限元近似.通过建立投影型插值算子各种形式的超收敛基本估计,证明了投影型插值算子的各类... 相似文献
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W空间中最佳逼近插值算子 总被引:11,自引:2,他引:9
一元函数有种种不同的插值方法,如多项式插值,样条插值,有理插值等,也给出了最佳插值算子[2]本文对二元函数讨论最佳逼近插值算子.设X是点集Ω上的实函数空间,是Ω上给定的一组点.由下式确定x上的一组泛函设Xu是X的。维子空间,定义X到Xu的算子Hn:其中(a;闪丹ZCXn.对X的子集人称dA【VI“fill_fillSlipwIVJ一【*un八V川UJXnCX{。。(Q)IVC。。irCh为A的逼近偏差.若某个n维子空IWXu达到(2)式的第一个下确界,则称此Xn为A的最佳逼近子空间,记为X:.X:中达到(2)式的第二个下确界的扣;(Q)}Z称为A的最… 相似文献
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本文研究了由高斯核构成的拟插值算子在闭区间上的近似逼近问题.利用函数延拓和近似单位分划的方法,构造了拟插值算子,并得到了一致范数下的逼近阶估计. 相似文献
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研究Banach空间中非光滑算子方程的光滑化拟牛顿法.构造光滑算子逼近非光滑算子,在光滑逼近算子满足方向可微相容性的条件下,证明了光滑化拟牛顿法具有局部超线性收敛性质.应用说明了算法的有效性. 相似文献
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对Banach空间X上的一个线性有界算子A,若存在一紧算子Q和一自然数m,使得‖A~m-Q‖<1,则称A是拟紧算子.本文使用算子谱理论的方法,从多个方面刻划了算子的拟紧性. 相似文献
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提出了一种基于Taylor算子的二元向量切触有理插值的新方法.首先应用已知的节点定义各阶有理插值基函数,再用相应的向量值和各阶偏导数值建立一种类似二元函数Taylor公式的新型插值算子,最后进行组合运算,得出二元向量一阶、二阶切触有理插值函数的显式表达式,并自然推广到k阶情形,还给出了误差估计.算例表明,该方法计算简单,过程公式化,有应用价值. 相似文献
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Fernando Cobos Luz M. Fernández–Cabrera Antón Martínez 《Mathematische Nachrichten》2007,280(15):1698-1708
We establish a formula for the measure of non‐compactness of an operator interpolated by the general real method generated by a sequence lattice Γ. The formula is given in terms of the norms of the shift operators in Γ. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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插值算子逼近是逼近论中一个非常有趣的问题,尤其是以一些特殊的点为结点的插值算子的逼近问题很受人们的关注.研究了以第一类Chebyshev多项式零点为插值结点的Hermite插值算子在Orlicz范数下的逼近. 相似文献
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本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理. 相似文献
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将经典“试探函数组”1,x,x^2应用于扩展乘数法,建立了一个判别线性正算子能否改造为逼近任何无界连续函数的充要条件。利用该条件给出了一类变形的插值多项式算子的收敛性定理,得到了具有一般性的结论。 相似文献
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《Mathematische Nachrichten》2017,290(11-12):1663-1677
We investigate interpolation properties of compact bilinear operators under the general real method. Results apply in particular to the real method with a function parameter and also to the complex method in the special case when the couple in the target reduces to a single Banach space or the source is a product of two fixed Banach spaces. 相似文献
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In this paper, we prove convergence rates for spherical spline Hermite interpolation on the sphere Sd−1 via an error estimate given in a technical report by Luo and Levesley. The functionals in the Hermite interpolation are either point evaluations of pseudodifferential operators or rotational differential operators, the desirable feature of these operators being that they map polynomials to polynomials. Convergence rates for certain derivatives are given in terms of maximum point separation. 相似文献
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The aim of this work is to apply the complex interpolation method to norms of n-tuples of operators in the p-Schatten classes of a Hilbert space H. The norms considered define Finsler metrics in a certain manifold of positive operators, and can be regarded as weighted p-norms, the weight being a positive invertible operator. As a by-product, we obtain Clarkson's type inequalities. 相似文献
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The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are bounded projections, and still they commute with the exterior derivative. In the present paper we generalize the construction of these smoothed projections, such that also non-quasi-uniform meshes and essential boundary conditions are covered. The new tool introduced here is a space-dependent smoothing operator that commutes with the exterior derivative.
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Luz M. FERNANDEZ-CABRERA Anton MARTINEZ 《数学学报(英文版)》2007,23(8):1357-1374
We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Г. 相似文献