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讨论Banach空间中有界线性算子的Drazin逆的扰动问题.利用Jiu Ding在2003年给出的广义Neumann引理,给出关于Drazin逆的一个新扰动定理,并给出误差估计,推广了文献中相应的扰动结果. 相似文献
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王志宏 《数学的实践与认识》1997,(4)
Leontief逆矩阵是投入产出分析的核心概念。研究直接消耗系数的扰动对Leontief逆矩阵的影响是投入产出分析中结构变动问题的重要议题。本文研究了在投入占用产出框架下,各部门的固定资产消耗对Leontief逆矩阵的变动影响。 相似文献
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我们利用分块技术得到了扰动后元素广义Drazin可逆的充要条件,还研究了Banach代数上广义Drazin逆的扰动以及给出了扰动界. 相似文献
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Hilbert空间中点投影到一仿射集上的误差分析 总被引:1,自引:0,他引:1
设H_1,H_2是相同数域上的Hilbert空间,T:H_1→H_2是具有闭值域的有界线性算子.本文给出了在Hilbert空间中点投影到-仿射集上的完整的扰动分析.||关键词##4扰动;;投影;;仿射集;;Moore-Penrose逆;;最小二乘解;;约化最小模 相似文献
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本文利用Hilbert空间中可逆算子的极发解定理,将误差估计中矩阵求逆条件数的最优性在Hilbert空间中进行推广,证明了线性有界算子A的求逆条件数K(A)=‖A‖A^-1‖在求算子扰动逆(A E)^-1的相对误差界中的极小性质,指出了算子求逆条件数在误差估计为仅与算子A有关的最佳常数值。 相似文献
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本文利用Hilbert空间中可逆算子的极分解定理,将误差估计中矩阵求逆条件数的最优性在Hilbert空间中进行推广,证明了线性有界算子A的求逆条件数K(A)=AA-1在求算子扰动逆(A+E)-1的相对误差界中的极小性质,指出了算子求逆条件数在误差估计中为仅与算子A有关的最佳常数值. 相似文献
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孔祥强 《纯粹数学与应用数学》2012,(4):516-522
利用矩阵的奇异值分解方法,研究了矩阵广义逆的扰动上界,得到了在F-范数下矩阵广义逆的扰动上界定理,所得定理推广并彻底改进了近期的相关结果.相应的数值算例验证了定理的有效性. 相似文献
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研究了Banach空间中广义逆的扰动问题.给出了广义逆稳定的一些新特征,进而证明了这些稳定性特征与广义逆的选取无关,并由此得到了广义逆作为集值映射是下半连续的充要条件. 相似文献
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关于Jacobi矩阵逆特征值问题的扰动分析 总被引:1,自引:0,他引:1
刘新国 《高等学校计算数学学报》2001,23(1):9-14
1预备 若不特别说明,本文沿用[6]中记号. Hochstadt于1967年提出如下问题[1]: 问题Ⅰ 给定两组实数{λ}nj=1=1和{μ}n=1i=1,满足构造一个n阶实对称三对角矩阵Jn,使得λ1,…λn为人的特征值,而Jn-1阶顺序主子阵的特征值为μ1,…,μn-1. 问题Ⅱ 给定一组实数{λj}nj=1,满足构造一个n阶全对称三对角矩阵Jn(s),使得Jn(s)的特征值为λ1,λ2,…λn. de Boor和Golub[4]提出如下问题: 问题Ⅲ 给定两组实数满足构造n阶实对称三对角矩阵J… 相似文献
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This paper introduces the Hartwig and Spindelb(o)ck decomposition for tensors and the definition of Tensor-core inverse.Then several properties and representations of Tensor-core inverse,are investigated.Further,we present some perturbation bounds for the Tensor-core inverse based on the T-product. 相似文献
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考虑如下代数特征值反问题: 问题 G(A;{A_k}_1~n;λ).设 A=(a_(ij)),A_k=(a_(ij)~((k))),k=1,…,n是n+1个n×n的实对称矩阵,λ=(λ_1,…,λ_n)是n维实向量且λ_i≠λ_j,i≠j.求n维实向量c=(c_1,…,c_n)~T,使矩阵A(c)=A+sum from k=1 to n (c_kA_k)的特征值是λ_1,…,λ_n. 这一问题是经典加法问题的推广.当A_k-e_ke_k~~T(e_k是n阶单位阵的第k列)时, 相似文献
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In this paper, we study the perturbation problem for oblique projection generalized inverses of closed linear operators in Banach spaces. By the method of the perturbation analysis of linear operators, we obtain an explicit perturbation theorem and error estimates for the oblique projection generalized inverse of closed linear operators under the T-bounded perturbation, which extend the known results on the perturbation of the oblique projection generalized inverse of bounded linear operators in Banach spaces. 相似文献
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Perturbation Analysis of Moore–Penrose Quasi-linear Projection Generalized Inverse of Closed Linear Operators in Banach Spaces 下载免费PDF全文
In this paper, we investigate the perturbation problem for the Moore–Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore–Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore–Penrose metric generalized inverse of bounded linear operators in Banach spaces. 相似文献
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魏益民 《数学年刊A辑(中文版)》2003,(1)
本文建立了群逆的扰动界,此界基于矩阵A的Jordan标准形和P-范数,其中P是非异矩阵满足 是非异上双对角阵且 当矩阵A和A+E有相同的秩且 较小时,得到了 较好的估计.在相同的条件下,研究了相容的奇异线性系统Aχ=b的扰动,给出了χopt=A#b扰动的上界,其中A#是A的群逆,χopt是最小P-范数解. 相似文献
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Nadica Mihajlović 《代数通讯》2020,48(4):1803-1818
AbstractIn this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14]. 相似文献
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《Linear algebra and its applications》2001,322(1-3):207-217
Some additive perturbation results for Drazin inverses are given. In particular, a formula is given for the Drazin inverse of a sum of two matrices, when one of the products of these matrices vanishes. Some special applications of this are also considered. 相似文献
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Jun Ji 《计算数学(英文版)》1989,7(4):327-333
Algebraic perturbation methods were first proposed for the solution of nonsingular linear systems by R. E. Lynch and T. J. Aird [2]. Since then, the algebraic perturbation methods for generalized inverses have been discussed by many scholars [3]-[6]. In [4], a singular square matrix was perturbed algebraically to obtain a nonsingular matrix, resulting in the algebraic perturbation method for the Moore-Penrose generalized inverse. In [5], some results on the relations between nonsingular perturbations and generalized inverses of $m\times n$ matrices were obtained, which generalized the results in [4]. For the Drazin generalized inverse, the author has derived an algebraic perturbation method in [6]. In this paper, we will discuss the algebraic perturbation method for generalized inverses with prescribed range and null space, which generalizes the results in [5] and [6]. We remark that the algebraic perturbation methods for generalized inverses are quite useful. The applications can be found in [5] and [8]. In this paper, we use the same terms and notations as in [1]. 相似文献