共查询到17条相似文献,搜索用时 46 毫秒
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设A是m×n(m≥n)且秩为n的复矩阵.存在m×n矩阵Q满足Q*Q=I和n×n正定矩阵H使得A=QH,此分解称为A的极分解.本文给出了在任意酉不变范数下正定极因子H的扰动界,改进文[1,11]的结果;另外也首次提供了乘法扰动下酉极因子Q在任意酉不变范数下的扰动界. 相似文献
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本文研究极分解和广义极分解.孙和陈提出的Frobenius范数下的逼近定理被推广至任何酉不变范数情形.得到了次酉极因子的一个新的表达式.通过新的表达式,我们得到了次酉极因子在任何酉不变范数下的扰动界.最后,讨论了数值计算方法. 相似文献
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关于特征值的Hoffman-Wielandt型相对扰动界 总被引:4,自引:0,他引:4
本文主要研究了关于特征值的Hoffman-wielandt型相对扰动界,改进了LiRC和Ipsen I等人关于这方面的相应结果. 相似文献
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本文研究酉不变范数不等式的问题.利用函数的凸性,得到关于矩阵酉不变范数的几个不等式,理论验证,证明了新不等式优于相关文献中的结果. 相似文献
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设A是m×n阶复矩阵,分解式A=QH称为A的广义极分解,如果Q是m×n阶次酉短阵和H是n×n半正定的Hermite矩阵.本文给出了广义极分解的一些性质和推广了有关近似极因子的相关结论. 相似文献
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利用凹函数和半正定矩阵的性质,讨论并且得到了一些矩阵Rotfel型范数不等式.另外,通过研究Hermitian矩阵和斜Hermitian矩阵和的特征值的模行列式的不等式,得到一些关于Hermitian矩阵和斜Hermitian矩阵和的范数不等式.推广了文献中的相关结果. 相似文献
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The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented. 相似文献
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加权极分解 总被引:1,自引:0,他引:1
In this paper, a new matrix decomposition called the weighted polar decomposition is considered. Two uniqueness theorems of weighted polar decomposition are presented, and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied. 相似文献
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Wen LI 《数学学报(英文版)》2005,21(6):1515-1520
In this paper, we present some new perturbation bounds for subunitary polar factors in a special unitarily invariant norm called a Q-norm. Some recent results in the Frobenius norm and the spectral norm are extended to the Q-norm on one hand. On the other hand we also present some relative perturbation bounds for subunitary polar factors. 相似文献
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In this article, we present some new perturbation bounds for the (subunitary) unitary polar factors of the (generalized) polar decompositions. Two numerical examples are given to show the rationality and superiority of our results, respectively. In terms of the one-to-one correspondence between the weighted case and the non-weighted case, all these bounds can be applied to the weighted polar decomposition. 相似文献
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In this paper, by generalizing the ideas of the (generalized) polar decomposition to the weighted polar decomposition and the unitarily invariant norm to the weighted unitarily invariant norm, we present some perturbation bounds for the generalized positive polar factor, generalized nonnegative polar factor, and weighted unitary polar factor of the weighted polar decomposition in the weighted unitarily invariant norm. These bounds extend the corresponding recent results for the (generalized) polar decomposition. In addition, we also give the comparison between the two perturbation bounds for the generalized positive polar factor obtained from two different methods. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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Hadamard积和酉不变范数不等式 总被引:9,自引:0,他引:9
设Mn,m是n×m复矩阵空间,Mn≡Mn,n.对于Hermite阵G,H∈Mn,GH表示G-H半正定.记A和B的Hadamard积为AB.本文证明了若A,B∈Mn正定,而X,Y∈Mn,m任意,则(XA-1X)(YB-1Y)(XY)(AB)-1(XY),XA-1X+YB-1Y(X+Y)(A+B)-1(X+Y).这推广和统一了一些现存的结果.设‖·‖为任意酉不变范数,I是单位矩阵.本文还证明了对于X∈Mn,m和A∈Mn,B∈Mm,若AI,BI,则函数f(p)=‖ApX+XBp‖在[0,∞)上单调递增. 相似文献
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In this article we focus on perturbation bounds of unitary polar factors in polar decompositions for rectangular matrices. First we present two absolute perturbation bounds in unitarily invariant norms and in spectral norm, respectively, for any rectangular complex matrices, which improve recent results of Li and Sun (SIAM J. Matrix Anal. Appl. 2003; 25 :362–372). Secondly, a new absolute bound for complex matrices of full rank is given. When ‖A ? Ã‖2 ? ‖A ? Ã‖F, our bound for complex matrices is the same as in real case. Finally, some asymptotic bounds given by Mathias (SIAM J. Matrix Anal. Appl. 1993; 14 :588–593) for both real and complex square matrices are generalized. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献