矩阵函数

In Chapter 4, using Newton series, we obtain a divided differences formula of composite functions, and give a matrix equivalent form of these composite functions. Moreover, we derive a divided differences for the reciprocal series.

第四章利用形式Newton级数得到了复合函数的差商公式，并给出复合函数的一个矩阵等价形式，从而得到一个反级数的差商公式。

By using the race matrix problem as an example, this paper gives a quick evaluation method of recursive functions.

本文以赛马矩阵为例，给出一种递归函数的快速计算方法，其要点是一个数组记录已算出的函数

Based on the Collins formula, the analytical propagation equations for a Gaussian beam through a multiple spatial filter system are derived by using the methods of the matrix decomposition and expanding the aperture function into a finite sum of complex Gaussian function .

以Collins衍射积分公式为基础，利用A0CD矩阵分解与物理实现的技巧，以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，推导出了高斯光束通过多级空间滤波器系统的传输方程，并用数值计算加以说明。

Secondly,the one-step and multistep methods of the precise integration algorithms arederived by means of the integration of functional matrix by parts and interpolation function,and some recursion schemes suitable for precise integration are obtained.

然后，以函数矩阵的分部积分法和插值函数为工具，推导出精细积分的单步法和多步法，给出了多种精细积分的递推格式。

The propagation equations for oblique and off-axial Gaussian beams passing through cat-eye optical lens are deduced by using the theory of matrix optics and expanding the aperture function into a finite sum of complex Gaussian functions.

运用矩阵光学理论以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，进一步推导了倾斜离轴高斯光束通过猫眼光学镜头的解析传输公式，通过数值计算分析得到了倾斜系数和离轴量对猫眼效应反射光光强分布的影响规律。

But the introduction of new basis functions also poses a new problem, that is, the complexity of computation of two matrixes' elements in the derivative generalized eigenvalue problem in NMM. Fortunately we found a recursive algorithm and solved it concisely.

在引入幅度基函数和斜度基函数后，广义特征值问题中矩阵元素的计算变的繁琐，我们运用一种递推算法简洁地解决了这个问题。

The upper-bound counts and the lower-bound counts of Bent functions are proposed by researching the Hadamard matrix, which decrease the searching space of Bent functions.

通过正规Hadamard矩阵研究给出了GF(2~n)上Bent函数计数的上下界，降低了Bent函数搜索的空间。

In this model, the Hamiltonian operator includes not only the anharmonic parameter, but also the dispersive parameters describing dipole-dipole interactions, reflecting the character of molecular stretching vibrations.

计算中引入的模型Hamilton算符所包含的描述U-F键非谐振动的参数λ和描述U-F键之间的偶极-偶极相互作用参数ε1，ε2由实验值得出，波函数|ψn〉按形式为|n，α〉=|n1〉|n2〉|n3〉|n4〉|n5〉|n6〉的基函数集展开，从而把复杂的Hamilton方程转化为简单的矩阵代数方程。

In the method, the symmetric positive semidefinite matrices are updated to approximate the Hessian matrices of the elemental objective functions and their sum to approximate the Hessian matrix of the objective function.

算法用对称半正定矩阵作为元素目标函数的Hessian阵的近似，使得其和仍然保持目标函数的Hessian阵的某种稀疏性。

The results show that the key of this algorithm is the solution of the integral operational matrix of orthogonal function.

研究结果表明：基于正交函数逼近法的分布参数系统参数辨识算法的关键在于正交函数正、反向积分运算矩阵的求解。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。