英语翻译1.A bound for the singular values can be immediately obtained by applying Theorem 2.1 to the relative difference between the eigenvalues of B and the eigenvalues of B+F using the remark in footnote 2.The result so obtained is equivalent ,

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英语翻译1.A bound for the singular values can be immediately obtained by applying Theorem 2.1 to the relative difference between the eigenvalues of B and the eigenvalues of B+F using the remark in footnote 2.The result so obtained is equivalent ,
英语翻译
1.A bound for the singular values can be immediately obtained by applying Theorem 2.1 to the relative difference between the eigenvalues of B and the eigenvalues of B+F using the remark in footnote 2.The result so obtained is equivalent ,up to second-order terms in F ,to the one proved by Demmel and Veselic[2] and is valid for any size of F because B is positive definite.Instead,in this section,we focus on applying Theorem 2.1 to the eigenvalue variation of matrix(26) under perturbations to prove the following theorem:
2.Previous additive Weyl-type relative perturbation bounds for singular values have been obtaind either without any reference to relative perturbation bounds for eigenvalues [2.9]or using relative bounds for eigenvalues of the positive definite matrices B.Theorem 2.1 allows us to deal with the indefinite eigenvalue problem of the Hermitian matrix (26) to obtain a new boumd (28) for the singular value problem.
We continue by comparing the boumd (28) with the following one obtained in [2],which we state as in [9,Corollary 3.2].

英语翻译1.A bound for the singular values can be immediately obtained by applying Theorem 2.1 to the relative difference between the eigenvalues of B and the eigenvalues of B+F using the remark in footnote 2.The result so obtained is equivalent ,
一种奇异价值观念的约束,可立即得到应用定理2.1的B之间的特征值和使用脚注2时作上述表示的B + F的特征值的相对差异.这样得到的结果是等价的,到第二阶项在F,由Demmel和韦塞利奇[2]证明了一,对任何规模的F有效,因为B是正定的.相反,在这一节中,我们着重在运用定理2.1的矩阵（26个特征值扰动的变化）,证明以下定理：
前添加剂外尔式的奇异值的相对扰动界已不是没有为特征值的相对扰动界参考算出[290]或使用的正定矩阵特征值的相对界限乙定理2.1使我们能够处理无限的特征值在埃尔米特矩阵（26）以获取问题的新boumd（28）的奇异值问题.
通过比较,我们继续在[2],这是我们在[9状态,推论3.2]得到以下一boumd（28）.

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