查询词典 The Matrix

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

Firstly, based on the stability criterion for the nominal discrete singular time-delay system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality with linear matrix equality constraint is established, which ensures that the resulting closed-loop system is regular, causal and robustly asymptotically stable, and the static output feedback controller is designed by the feasible solution of the linear matrix inequality with linear matrix equality constraint.

首先基于标称离散广义时滞系统的稳定条件，以受限线性矩阵不等式形式，得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件，同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法；然后采用矩阵的正交补，把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解；最后的数值实例说明了所给方法的有效性和正确性。

According to the studied results at present, the studied objects are mainly thin plate and beam about sound radiation mode, a method computed sound radiation mode of complex structure is presented in this dissertation, according to the results of the previous two chapter, a theoretical method to solve acoustical radiation mode and acoustical radiation efficiency of complex structure by boundary element method and acoustical radiation theory is posed, the acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regard to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results. According to results of the form three chapter, the structure sound radiation sensitivity is studied in detail, the sound radiation power of structure can be expressed as positive Hermitian quadratic form, the sound radiation sensitivity can be expressed as two parts by partial differential with respect to design variable, which are sensitivity of boundary velocity and impedance matrix, combined with the theory of FEM and BEM, the structure sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. The theory posted in this dissertation is tested by the FEM software ANSYS and the software AAS programmed by author.

在前几章的基础上，通过结构声辐射的模态理论对结构的声辐射的机理进行了深入地探讨，针对目前声辐射模态的研究对象主要是简单的板和梁类结构，提出了一种计算复杂结构声辐射模态的方法，利用前两章研究所得的结论，将边界元方法与广义特征值的理论结合起来研究了复杂结构的声辐射模态与声辐射效率，先将结构的声辐射功率表示为一个正定的厄米特二(来源：ABb7C论文0909网www.abclunwen.com)次型，运用广义特征值分解求解了复杂结构的声辐射模态，然后利用声辐射模态关于阻抗矩阵与均方速度耦合矩阵的正交性，求解了复杂结构的声辐射效率，最后用具有解析解的脉动球与辐射立方体验证了该方法的有效性。

Unlike the previous method, however, the proposed algorithm obtains the new transformed matrix by taking the conjugate operation to the forward and backward spatial smoothing covariance matrix of the received data, so that the modified covariance differencing matrix which is a Hermitian matrix of zero real part can lower the computation load effectively during the eigenvalue decomposition.

不同于以前的算法，提出的算法通过对接收数据的前后向空间平滑协方差矩阵进行共轭运算得到新的变换矩阵，因此修正后的协方差差分矩阵是个实部为零的厄米特矩阵，从而有效地降低了特征分解过程的计算量。

The using of the technologies of DOA in the orientation estimating of interference is discussed, then an evolutive ESPRIT algorithm is put forward which avoids the eigendecomposition and is easily achieved. To the MUSIC algorithm, an easy eigendecomposition algorithm for Hermitian matrix is presented. It breaks away form the complex matrix decomposition such as QR algorithm. Basing on the whole matrix, the algorithm makes use of the multiplication operation of matrix and vector, which attains simpleness and is fit for DSP. In the field of DOA estimating of correlation interferences, spatial smoothing algorithm consumes too many array units.

讨论了DOA技术在干扰源方位估计中的应用，提出了一种ESPRIT演变算法，该算法避开了特征值分解，实现简便；在MUSIC算法的实现中提出了一个Hermitian矩阵特征值分解算法，该算法摆脱了复杂矩阵分解，从矩阵整体出发，主要的运算是矩阵与矢量的乘运算，算法简单，非常适合DSP芯片实现；在相关源的DOA估计中，空间平滑技术使阵元的损失非常大，本文提出了一种进一步降低阵元消耗的平滑技术—随机空间增益法，其在运算量上的增加很小，但对于相干源的去相关确是有效的。

Then, we set up the double-row monodromy matrix of the Hamiltonian, the transfer matrix and the reflection equation of the system with the help of the scattering matrix and the reflecting matrix.

接着借助量子反散射方法，运用两体散射矩阵和反射矩阵，构造了双行monodromy矩阵、转移矩阵和系统的边界反射方程，从而详细证明了系统的精确可解性。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

The analysis of the optical signal transmission characteristics and the physical parameters provides the theoretical foundation for optimizing the design and improving the performance of AWG; and the optimizing design numerical value calculation method solves the complex problem of the optimizing design of the AWG, it can also provide a way for AWG computer aided design system; the AWG optical signal processing analysis provide a way for optical signal Fourier transform, serial and parallel transmission, circle shift, matrix transform and differential processing; the optical signal processing characteristics of AWG develop AWG to use for new field, and the optical signal processing will play an important role on all-optical networks in the future; by the definition of the wavelength transform matrix of the AWG, the signal output positions that come from these input signals of the different wavelength or the same wavelength but the different input ports and carrying different signals can be accurately determined, and the wavelength transmission matrix plays an important role for analyzing the routing of the complex optical network, or designing the network nodes such as the optical path add/drop multiplexer and optical cross connect device; the wavelength transmission matrix also provides a method for monitoring and managing the wavelength transmission of the optical network nodes; e analysis of the AWG' OXC node structure and wavelength routing provides a way for realizing the OXC, especially for multi-path/multi-wavelength OXC and the intelligence node of the optical networks; by the studying of the control plain characteristics, router, traffic engineering, program and the improved arithmetic of the wavelength routing, the method for realizing the GMPLS' OXC optical transport network is provided, and it play an important role for the study of the automatic switched optical network; the time-frequency analysis can provide more information about the dispersion and energy changes of .the pulsed light transmission in the singlemode fiber, it also provides more useful parameters for analyzing the dispersive accumulating and dispersive compensating.

AWG光信号传输特性与相关参数的分析，为进一步优化设计AWG及提高其性能提供了理论依据，而优化设计计算数值方法解决了AWG优化设计计算的复杂问题，为进一步建立AWG的计算机设计系统提供了基础；AWG光信号处理的特性分析，提出了AWG应用的新领域，为光信号的傅立叶变换、串并传输、循环移位、矩阵变换、微分处理等提供了一条途径；波长传输矩阵变换关系的建立，不仅得到了确定多路AWG每路信号从输入端口到输出端口的准确输出位置的方法，而且在分析应用AWG实现复杂的光通信网络路由的连接、特别在设计分插复用器和交叉连接器等网络节点时有重要的作用，能有效而准确地确定波长的路由关系，为实现节点波长传输路由的监控和管理提供有效手段；基于AWG的OXC结构和波长路由的确定为实现OXC技术、特别是多路多波长的OXC和光网络的智能节点技术提供了有效的方法；控制平面的特征、路由器、流量工程、程序及改进的波长路由算法的研究实现了基于GMPLS的OXC光传送网络的控制平面，为建立自动交换光网路提供了一定的基础；时频分析可以更直观和更清晰地描述脉冲信号在单模光纤中传输色散和能量的变化，为色散积累和色散补偿提供有效的分析参数。

Taking the active network as a research task, the input accessibility, the Coates graph of matrix and graph transmission etc are used to analyze the relation between reducibility of the coefficient matrix of the state equation and the electric separability of the network or the electric accessibility of the network for the first time, acquiring sufficient and necessary conditions that coefficient matrix of the state equation is reducible. Network Graph Theory, Matrix Theory and System Theory over F etc are used to derive the structural controllability criterion of the passive network over F for the first time. Then according to these theoretic results, the structural controllability problems of the active network over F are studied, acquiring several structural controllability conclusions of the active network.

率先将状态方程的输入可达、矩阵的Coates图、流图传输系数等概念和方法引入到对F上有源电网络的研究，研究了网络状态方程的系数矩阵的可约性与网络电气可断性或电气可达之间的关系，研究了F上有源电网络的能控性问题，获得了状态方程的系数矩阵可约的充分必要条件、F上有源电网络系统的结构能控性判据等新的结论。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。