查询词典 least squares

Least-squares solution for the inverse problem of real matrices、symmetric matrices and bisymmetric matrices are studied in this thesis. The thesis includes the following contents.

本文研究了子阵约束下实矩阵、实对称矩阵和双对称矩阵反问题的最小二乘解，全文主要包括以下内容。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

Model updating; modal parameter; centrosymmetric; iterative method; least squares problem; quadratic constraint

模型修正；模态参数；中心对称矩阵；迭代法；最小二乘问题；二次约束

As a case in this study, there is a non–representative PK duality model which adopts the least squares method or even the Monte Carlo method to estimate their parameters. Using yield frequency analysis to recommend fertilization, only a group of P and K coenobium, the sixth treatment, meets the conditions of goal yield.

对Monte Carlo法也不能得到典型式的晚稻磷钾非典型肥效模型，用产量频率分析法计算推荐施肥量，表明只有一组磷钾肥用量组合入选，导致磷肥推荐用量偏高而钾肥偏低。

In the research of techniques in curved surface reconstruction and feature extraction, the modeling of NURBS interplation curved surface based on rectangular is focused, in which centripetal parameter is applied to construct node vector, the application of interplation method guarantees the accuracy of curved surface construction, bicubic NURBS curved surface is taken as an example to demonstrate the process of curved surface modeling, and the effectiveness of NURBS is approved in application; Meanwhile, the application of feature techniques in reverse engineering is also diSCUSSed, the recognition and extraction method of feature curved surface are investigated, the relationship between feature recognition and the curvature of curved surface is discussed, with the application of linear and non-linear least squares procedure, data fitting of conicoid in ball surface, cylinder surface and cone surface is

以上述的研究工作为基础，根据企业的实际需求选定轻客和重卡作为研究对象完成了基于反求工程的车身改型设计和优化的工程实践，通过工程实践对反求工程各关键支撑技术进行了验证，所开发的新车型也获得了良好的市场反应。

According to the least-squares procedure the thickness inaccuracy and the errors of roundness,cylindricity,and coaxiality will be obtained.

整机在计算机控制下，实现X，Z，C方向的运动。测量开始前，在旋转工作台1上用夹具2将弹体3固定，两个激光位移传感器6和7，安装位置如图所示。

The cylindricity could be calculated by least squares method and wavelet error separation method that the measurement error could be decomposed by Harmonic analysis algorithm based on wavelet theory.

针对激光 CCD 灵敏度高，干扰噪声容易混入测量数据中的问题，提出了一种基于小波分析的误差分离方法，即运用谐波分析的思想方法和小波理论中多频率分析算法进行误差分离，误差分离后的数据用最小二乘法处理求出圆柱度。

Four methods for evaluating circularity error. least-squares method for evaluating cylindricity error. 3.Using language of VC++, a software of form error evaluating is developed. Module structure is adopt in this software and every element has one module.

用VC++开发了形状误差的评定软件，软件采用功能模块结构，每种元素均设计为一个独立的模块，为使评定结果更加直观，采用OpenGL对处理的结果进行了可视化处理，结果图形可以随意转动和缩放，以方便观察。

The successive stability constants which are obtained by non-linear least-squares methord fitting Bjerrum formula. In three- system ,the results from Scatchard plots indicate that there exists two strong binding site of Mn and one strong binding site of Zn,there are same results compareing with two -system ,but some more weak binding sites are different from the different addition sequence ,show that there are not common strong binding site of Mn,Zn in HSA or BSA .Strong binding sites have electiveness and unfalteringness ,weak binding sites exists irreversibility.

用非线性最小二乘法拟合Bjerrum方程，计算了同时竞争体系的逐级稳定常数；Scatchard图分析表明，三元体系中，Mn和Zn与血清白蛋白结强合部位数分别为2和1，与二元体系相比，保持不变，弱结合部位数随加入顺序的不同而不同，但都有所增加，竞争结果说明了Mn和Zn与血清白蛋白结合没有共同的强结合部位，强结合部位具有专一性，选择性，而弱结合部位具有不可逆性。

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。