范数

Meanwhile, we also provide methods for computing the weighted polar decomposition, and study error bounds for the approximate generalized positive semidefinite polar factor and perturbation bounds for weighted polar decomposition in various norms.

针对这个新的矩阵分解，我们证明了其唯一性定理，给出了其唯一性条件，讨论了其极因子的最佳逼近性质；同时，我们还探讨了矩阵加权极分解的计算问题，研究了由迭代算法引起的极因子的误差界，极因子在各种范数下的各种形式的扰动界等。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

The second part includes the definition of positive definite function and conditional positive definite function, the basic form of Radial Basis Function interpolation, the correctness of the inversion of the interpolation matrix, the error estimate based on Kringing function.

主要包括径向基函数的相关定义，基本的插值形式，插值矩阵的可逆性，以Kringing范数为基础的径向基函数插值的局部误差估计和径向基函数插值边界附近的情况。

The principal component method and the minor component method are recommended to reduce the computation of MNE and MPE respectively. Whether rank reduction conducted or not, STAP is always performed in a particular space which may be spanned or expressed by different sets of basis.

我们在第5章讨论了DFP结构上两种特征子空间降维方法，即最小功率特征对消和最小范数特征对消，这两种方法将权矢量约束在噪声子空间内，从而能够对消与噪声子空间正交的杂波分量。

In the optimal control of kinematics for redundant robots, two new concepts, the matrix weightability measure and the self-motion declinability measure are proposed. Further, a modified weighted gradient projection method which combines gradient projection method with weighted least-norm solution is presented, it can attain ideal optimal effects at low velocities.

本文对冗余自由度机器人的运动学、动力学和容错等方面的优化控制进行了深入的分析和探讨：在冗余度机器人运动学优化控制方面，提出矩阵可加权度和自运动可衰度的概念，将梯度投影法和加权最小范数解法有机的相结合，形成可优化能力强、关节速度较低的改进的加权梯度法。

Questions about norms and spectra are likely to be recalcitrant .

有关范数和谱的问题多半是难解的。

Browkin and so on, an available method to get improved bounds for the norm of exceptional places in computing K〓 groups for the ring of integers in quadratic imaginary fields is obtained and as an application, K〓Z is determined.

Browkin等人工作的基础上，得到了估计虚二次域整环的K〓群的计算中例外位的范数的界的较有效的方法，并且作为应用，确定了K〓Z。

Robust goodness-of-fit test of AP model based on L-1 norm fitting［J］.

基于L-1范数拟合的AR模型的稳健的拟合优度检验［J］。

Robust goodness-of-fit test of AR model based on L-1 norm fitting .

基于L-1范数拟合的AR模型的稳健的拟合优度检验。

A method of calculating the adaptive scale control parameter is introduced.

实验表明，该算法无论从信噪比改善量还是视觉效果都要优于规整化项为单一范数的复原方法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。