共查询到19条相似文献,搜索用时 546 毫秒
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该文引进Ba空间多元加权光滑模,推广L^p空间的DitzianTotik模, 证明该模与K泛函的等价性. 作为应用,讨论定义在单纯形上多元Bernstein-Durrmeyer算子与多元加权光滑模之间的关系. 即以多元加权光滑模为尺度, 建立Bernstein-Durrmeyer算子在Ba空间逼近阶的上界与下界估计. 相似文献
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本文建立了Shepard-Lagrange算子逼近的正逆定理,证明了可以利用高阶光滑模来刻画Shepard-Lagrange算子的逼近性质.从而说明了Shepard-Lagrange算子比一般的Shepard算子具有更好的逼近性质.进一步,所用光滑模的阶梯函数非常广泛,这是多项式逼近所不具有的. 相似文献
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本文提出了求解张量互补问题的一类光滑模系矩阵迭代方法.其基本思想是,先将张量互补问题转化为等价的模系方程组,然后引入一个逼近的光滑函数进行求解.我们分析了算法的收敛性,并通过数值实验验证了所提出算法的有效性. 相似文献
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为了改进求解大型稀疏线性互补问题模系多重网格方法的收敛速度和计算时间,本文采用加速模系超松弛(AMSOR)迭代方法作为光滑算子.局部傅里叶分析和数值结果表明此光滑算子能有效地改进模系多重网格方法的收敛因子、迭代次数和计算时间. 相似文献
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本文利用点态光滑模Bernstein-Durrmeyer算子的r阶级性组合的逼近进行了研究,统一了已有的关于古典光滑模和Ditzian-Totik 模的结果. 相似文献
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首先介绍了由Young函数生成的Orlicz空间L_Φ~*[0,∞),然后利用归纳假设和分解方法证明了r阶加权光滑模与加权K-泛函的等价性,最后作为光滑模的应用给出了Gamma算子在L_Φ~*[0,∞)空间内加权同时逼近的B-型强逆不等式. 相似文献
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引入了一类修正的Lupas-Durrmeyer型算子,该算子不仅常数保持还线性保持.利用连续模,光滑模和K-泛函,讨论了该算子的某些逼近性质.最后还给出了该算子对Lipschitz函数类的逼近及Voronvskaya型渐近展开公式. 相似文献
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Ramazan Akgün 《复变函数与椭圆型方程》2019,64(2):330-351
Mixed modulus of smoothness in weighted Lebesgue spaces with Muckenhoupt weights are investigated. Using mixed modulus of smoothness we obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. Also we obtain equivalences between mixed modulus of smoothness and K-functional and realization functional. Fractional order modulus of smoothness is considered as well. 相似文献
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Ding-Xuan Zhou 《Results in Mathematics》1995,28(1-2):169-183
This paper investigates global smoothness preservation by the Bernstein operators. When the smoothness is measured by the modulus of continuity, this problem is well understood. When it is measured by the second order modulus of smoothness, H. Gonska conjectured that the Lipschitz classes of second order keep invariate under the Bernstein operators. Here we present a counterexample to this conjecture. Then we introduce a new modulus of smoothness and show that the Lip-α(0 < α ≤ 1) classes measured by this modulus are invariate under the Bernstein operators. By means of this modulus we also improve some previous results concerning global smoothness preservation. 相似文献
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球面上Peetre K-模和最佳逼近 总被引:1,自引:0,他引:1
本文研究了球面上三种PeetreK-模与最佳逼近的关系,建立起它们之间的若干强型和弱型不等式.此外,还讨论了K-模与光滑模的等价性. 相似文献
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The purpose of this paper is to present a characterization of certain types of
generalized weighted Peetre K-functionals by means of a modulus of smoothness.
This new modulus is based on the classical one taken on a certain linear
transform of the function. A new modulus of smoothness which describes the best
algebraic approximation is introduced. 相似文献
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This paper concerns about the approximation by a class of positive exponential type multiplier operators on the unit sphere Sn of the (n + 1)- dimensional Euclidean space for n ≥2. We prove that such operators form a strongly continuous contraction semigroup of class (l0) and show the equivalence between the approximation errors of these operators and the K-functionals. We also give the saturation order and the saturation class of these operators. As examples, the rth Boolean of the generalized spherical Abel-Poisson operator +Vt^γ and the rth Boolean of the generalized spherical Weierstrass operator +Wt^k for integer r ≥ 1 and reals γ, k∈ (0, 1] have errors ||+r Vt^γ- f||X ω^rγ(f, t^1/γ)X and ||+rWt^kf - f||X ω^2rk(f, t^1/(2k))X for all f ∈ X and 0 ≤t ≤2π, where X is the Banach space of all continuous functions or all L^p integrable functions, 1 ≤p ≤+∞, on S^n with norm ||·||X, and ω^s(f,t)X is the modulus of smoothness of degree s 〉 0 for f ∈X. Moreover, +r^Vt^γ and +rWt^k have the same saturation class if γ= 2k. 相似文献
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Jiang Hong-Biao 《东北数学》2009,25(4):289-298
In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ (f,t)p. Cuo extended the MiiUer's results to wφ^24 (f, t)∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem. 相似文献
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Taylor-Delsart formula is elaborated in the paper for functions of the generalized Gegenbauer shift. This formula is utilized to construct a version of the Gegenbauer shift modulus of smoothness of order k which for k = 1 reduces to the modulus of smoothness of the first order. By means of this modulus and Peetre’s K-functional, an interpolation theorem is obtained. Equivalent normalizations are obtained for functional spaces associated with the generalized Gegenbauer shift. 相似文献
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St. J. Goebbels 《Results in Mathematics》2013,63(1-2):311-327
This paper discusses the approximation of Fourier coefficients by Fourier Lagrange coefficients. It gives an error bound in terms of an averaged modulus of smoothness. The sharpness of this estimate is shown as an application of a quantitative resonance principle by utilizing the aliasing phenomenon that occurs in the context of discrete Fourier transformation. The scenario is used to compare the averaged modulus with classical uniform and integral moduli of smoothness. 相似文献
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Ioan Gavrea 《Journal of Computational Analysis and Applications》2001,3(3):249-257
We investigate the global smoothness preservation by Bernstein operators measured by second-order modulus of smoothness and give a partial answer for a conjecture raised by H. H. Gonska in 1998. 相似文献