逆计算

The characteristic, difference and relation of the normal and inverse design are compared detailedly. The formula of the first and second class eigen sensitivity are given. For the horizotal vibration system of building structure, the sensitivity method and perturbation method are adopted to modify the dynamic characteristics. The inverse eigenvalue problem of Jacobi matrix and the positive, symmetry, band matrix are studied. The method of Evolutionany Computation is first used in the inverse design of building structure, the principal problems are studied. The features of aseismatic inverse design of building are analysed.

本文较详细地比较了正、逆设计的特点；给出了特征值和特征向量的一阶和二阶灵敏度分析公式；对于建筑结构水平振动系统，提出了结构动态特征的修改方法；对Jacobi矩阵及实对称带状矩阵的逆特征值问题进行了分析研究，首次将其引入建筑结构抗震逆设计中；首次将进化计算方法应用于建筑结构抗震逆设计中，对主要问题作了探讨；对建筑结构抗震逆设计的特点进行了分析，提出未来的发展方向和前景。

The aim of this paper is to study the generalized inverse of matrices on rings, the generalized inverse of morphism and partial ordering of matrices.

矩阵广义逆的研究包括环上矩阵的广义逆，范畴中态射的广义逆，广义逆矩阵的计算和广义逆矩阵的应用等。

Telante method using the inverse matrix calculation and numerical simulation.

用特兰特方法进行矩阵的求逆计算和数值模拟。

By reduction of inverse operation, the efficiency of the filter in each channel is improved.

通过减少重复求逆计算，提高各通道逆滤波器的效率。

And then, this paper presents an algorithm of computing the left inverse or right inverse for these special rectangle matrices. In thenormal algorithms for solving these problems, we need O(m2n) multiplications ordivisions. The algorithms in this paper only need O + O(n2) multiplications ordivisions. The paper is built as follows.

常规的计算m×n阶不相容线性方程组的极小范数最小二乘解的算法所需计算量为O(m~2n)，而本文根据特殊矩阵的特殊结构，通过两种不同的构造方式给出了两类不同的计算极小范数最小二乘解的快速算法，并给出了求特殊矩阵的左逆及右逆的快速算法，它们的计算量均为O+O(n~2)。

Those problems include inverse position analysis of the machine, inverse and direct position analysis of the parallel locking mechanism, relationships of velocity and acceleration between cutter and actuators, Jacobian matrix of the machine, forward position computation of the machine, the links'velocity and acceleration of the driving chains, the links'velocity and acceleration of the locking mechanism, kinematics simulation of the machine, and so on. The Jacobian method presented in the thesis to calculate the direct position of the machine is of high efficient.

其中包括机床的位置逆解分析，平行机构的位置逆解分析，机床刀具与各主动关节之间的速度和加速度映射关系的求解，并联机床雅可比矩阵的计算，并联机床的位置正解计算，支链构件的速度和加速度计算，平行机构各构件的速度和加速度计算以及机床各运动学指标的仿真计算等。

The second chapter discussed the definition and nature of dashes inverse A in generalized inverse as well as its application in compatible linear equations. The third chapter discussed the definition and calculation of the minimum norm inverse A in generalized inverse, as well as the Minimal Norm Solution of its compatible linear equations Ax = b.

前言从引进广义逆矩阵的定义着手，介绍了它的历史概况以及发展的背景及其意义；第1章从广义逆的发展历程讨论由Moore-Penrose方程确定的各种广义逆的定义；第2章讨论广义逆中的减号逆A 的定义及性质以及在相容线性方程组的应用；第3章讨论广义逆中的最小范数逆A 的定义及计算以及它与相容线性方程组Ax=b的极小范数解。

The preface gave the definition and introduced history, background of development and significance of generalized inverse matrix. The first chapter, from the development process of generalized inverse, discussed all kinds of definition of generalized inverse determined by the Moore - Penrose equations. The second chapter discussed the definition and nature of dashes inverse A in generalized inverse as well as its application in compatible linear equations. The third chapter discussed the definition and calculation of the minimum norm inverse A in generalized inverse, as well as the Minimal Norm Solution of its compatible linear equations Ax = b.

前言从引进广义逆矩阵的定义着手，介绍了它的历史概况以及发展的背景及其意义；第一章从广义逆的发展历程讨论由Moore-Penrose方程确定的各种广义逆的定义；第二章讨论广义逆中的减号逆A 的定义及性质以及在相容线性方程组的应用；第三章讨论广义逆中的最小范数逆A 的定义及计算以及它与相容线性方程组Ax=b的极小范数解。

The calculation based on the quasi conforming element method is the exact solution of generalized compatibility equations and satisfies the weak continuity requirement naturally,and in the calculation,which does not need satisfy stress equilibrium conditions,the calculating process of the matrix's inverse is simplified.

拟协调元不需要应力满足平衡条件，简化了矩阵求逆计算，容易得出应变的离散精度，因此可以解决常规有限元难以适应的领域，对计算力学发展起着重要的作用。

In section 3, on the base of the iterative algorithm, we obtain a new iterative algorithm which is convergent to the signal faster than the old one. In section four, if the form of φ is simple and the sampling set is the integer set Z, then a direct reconstruction formula is presented.

在第二节，我们通过计算对偶框架来重建信号，这与传统的计算对偶框架方法不一样，该算法是通过计算一个矩阵的逆矩阵来计算对偶框架，当矩阵是奇异矩阵时，可通过奇异值分解方法或截断奇异值分解算法来求矩阵的广义逆矩阵。

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。