本文推导了使用常单元和线性单元时矩阵元素的解析表还式，从而避免了数值积分。
This paper derives the analytical formulas for elements of the matrices using constant and linear elements Therefore, the numerical integral can be avoided.
它是基于数值积分和矩阵最小二乘法的数值方法。
It is based on the numerical integration and matrix least square method.
在卫星的状态估计过程中应用推广的序列估计算法，借助数值积分方法积分状态向量和协方差矩阵。
For the estimation of satellite state, the extended sequential estimation algorithm was applied. The numerical method was used to integrate state vector and error covariance matrix.
ADAMS采用拉格朗日动力学方程，辅以刚性积分算法以及稀疏矩阵技术来求解模型。
ADAMS solves the model by adopting Lagrange dynamics equation and complementing with rigidity integral algorithm and sparse matrix technology.
进而将积分方程形式的特征值问题转化为无穷阶矩阵的标准特征值问题。
And the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order.
文中导出了四种情况下刚度矩阵的简化计算公式，这些公式比对应的高斯积分算法节省计算工作量94—98%。
Simplified formulae for computing the stiffness matrices in four cases are derived, which, compared with corresponding Gauss integration algorithm, can cut 94-98% computing time.
通过将动态矩阵比例积分控制算法与串级控制相结合，提出了一种新的火电厂锅炉过热汽温控制方案。
A new superheated steam temperature control system is derived by combining the dynamic matrix proportion integration control arithmetic with the cascade control structure.
得到了根据插值函数来计算刚度矩阵秩的计算公式，并对几种降阶积分单元进行了验算。
A formula based on the interpolation for the rank of the element stiffness matrix is presented, and some reduced integration elements are examined.
在原有精细积分法的基础上，对非齐次方程出现奇异矩阵的问题进行探讨。
Based on the original precise integration method, the problem that singular matrix appears in non-homogeneous equation was discussed.
利用广义函数给出了一种精确积分方法，可以得到有关矩阵的显式表达，得到提高了求解精度和效率。
By using generalized function, an accurate integration method is developed to get the explicit formulation of the matrixes involved. This can improve the accuracy and efficiency of the method.
导出了正向和逆向积分的运算矩阵。
Operational matrices for forward and backward integrations have been derived.
Q3D提取使用的矩量法(积分方程)和有限元计算的电导，电容，电感和电阻矩阵。
Q3D Extractor USES method of moments (integral equations) and FEMs to compute capacitive, conductance, inductance and resistance matrices.
通过积分变换的方法可以求出每一层表面处位移与力之间的关系，进而形成层刚度矩阵。
The layer stiff matrix, which expresses the relation of force and displacement on surface of every layer, could be calculated to apply integral transformation.
从光线矩阵元表达的衍射积分出发，导出了复杂光学系统的光学传递函数。
Starting from the diffraction integration in terms of ray matrix elements, the optical transfer functions have been derived for complicated optical system.
进而将积分方程形式的特征值问题转化为无穷阶正定对称矩阵的标准特征值问题。
And then the eigenvalue problem of integral equation is transformed into the standard eigenvalue problem of a positive definite matrix with infinite order.
采用矩阵分解的方法，从柯林斯衍射积分公式出发，对高斯光束通过失调空间滤波器的传输特性进行了分析，得到了相应的解析式。
Based on the method of matrix decomposition, and the Collins diffraction integral formulae, the propagation characteristics of a Gaussian beams passing through misaligned spatial filter are studied.
对复杂光学系统证明了光线矩阵元表达的衍射积分是旁轴波动方程的准确解。
It is proved in a complicated optical system that the diffraction integration in terms of ray matrix element is the right solution 'for paraxial equation.
形成单刚矩阵时，不需要在单元域内进行数值积分，容易构造曲边单元。
The numerical integral is not needed in forming element stiffness matrix by the present method. It is easy to constructed curved element.
利用广义拉盖尔多项式的级数表达式和分步积分法，给出了各向同性谐振子径向矩阵元的另一种表达式。
Another expression of the radial matrix elements for isotropic harmonic oscillator is obtained by using progressional expression of the generalized Laguerre polynomial and the partial integration.
绩效矩阵；模糊测度；模糊积分；qs- 9000系统。
Performance matrix; fuzzy measures; fuzzy integrals; QS-9000 system.
周期时变线性系统系数矩阵的时变性与不可交换性是其精细积分算法设计中的瓶颈。
The time-varying and incommutable character of the coefficient matrix of periodically time-varying linear systems are the bottleneck of the design for high precision direct integration methods.
采用积分变换和传递矩阵方法，求解了成层土在内部环形荷载作用下的基本解；
The fundamental solutions for displacements and stress components of the layered soil due to unit internal ring loading are first derived with integral transforms and the transfer matrix method.
本文在严格、完整的基础上，利用矩阵范数理论研究了结构非线性动力分析中数值积分格式的稳定性问题，给出了判别单自由度非线性动力方程积分格式稳定性的一般数学准则。
The problem of stability in the numerical integration schemes of nonlinear dynamic analysis of structures is discussed by using matrix and norm theory on a rigorous and complete basis in this paper.
然后，由虚功原理推导出了整体平衡方程中的广义刚度矩阵和荷载向量的具体表达式，并对其数值积分方法进行了讨论。
Then, the generalized stiffness matrix and load vector in the equilibrium equations are formulated by using the virtual work principle, and the numerical integration method is discussed.
与更新精细积分法相比，在实现动力微分方程降阶后，矩阵尺度和方程个数减少一半；
When the order of dynamic differential equation is reduced, the size of matrices and equations of the proposed method are only half of that of the RPTSIM.
推广的序贯估算法有两种形式：1。积分误差协方差矩阵，2。积分状态转移矩阵。
There are two forms of extended sequential estimation algorithm: 1. integrating error covariance matrix; 2. integrating state transition matrix.
该方法通过一系列特解来建立边界积分方程，从而避免了其系数矩阵的直接计算。
The method is used to build the boundary integral equation by a serious of particular solutions. It can avoid calculating the coefficient matrix directly.
计算积分的方法、复数方法、无线级数、奇殊函数、微分方程、向量及矩阵、群论。
Methods in evaluating integrals, some complex variable methods, infinite series, special function, ordinary differential equations, vector and materials, groups and group representations.
将逐步积分法的思想与传统传递矩阵法相结合，提出了增量传递矩阵方法。
An increment transfer matrix method based on step-by-step integration method and traditional transfer matrix method was put forward.
将逐步积分法的思想与传统传递矩阵法相结合，提出了增量传递矩阵方法。
An increment transfer matrix method based on step-by-step integration method and traditional transfer matrix method was put forward.
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