| 1. | Over - determined system
超定系统 |
| 2. | Approaches for solving the super - posed boundary value problem by using the data provided on two different
联合两个界面的数据求解超定边值问题的途径 |
| 3. | Over - determined model for computing gravity anomaly based on regularization solution of discrete integration eguation
基于积分方程正则化的重力异常超定问题解法 |
| 4. | The sirt inversion operator can be applied to solve the large - scale sparse linear equation and velocity tomographic inversion can be performed based on direct arrival traveltime and accuracy could be 3 meters
研究成功的sirt反演算法可用于求解大型稀疏超定线性方程组，根据直达波旅行时进行速度层析反演，其精度可达到3米。 |
| 5. | The series of point group calculated by this algorithm theory is strictly descending and converging to the stable polar point . this theory is very efficiency in solving the problem of lad for its simplicity 、 rapid speed and high adaptability
本文算法所产生的点组序列是严格下降并收敛于稳定极点的，我们的计算表明，本算法对求解超定最小一乘估计问题非常有效，具有算法简单、速度快、适应性强的特点。 |
| 6. | The water quality respond relation of input - output measurements are established by systematic theory in this paper . according to the peculiarity of hydrology and the necessity of water quality inverse problem the multi - parameter inverse problem model based on ordinary differential equation is developed . the existence and uniqueness of the solution of the ordinary differential equation about two parameters or multi - parameter are to be proved . the unstability depending on errors between monitoring data and interpolation approximate data are analyzed and demonstrated . cubic spline interpolation function , the least two multiply and positive rule method are conjoined for obtained solution of multi - parameter . the results from this algorithm indicats its efficient to the multi - parameter identification in water quality modeling
本文应用系统理论，建立了水质多参数输入输出之间的响应关系；根据河流水文水质变化特点和参数反问题的需求，建立了水质常微分方程多参数反问题模型.根据常微分方程参数反问题的数学理论，作者给出了两参数和多参数水质常微分方程反问题的解的存在性、唯一性的理论证明过程和结论；还针对水质现有监测资料的测验误差和插值近似计算误差造成参数反问题的不稳定性，将三次样条插值函数、超定方程最小二乘法和正则化算法有机地结合使用，成功地给出了水质参数反问题的稳定化算法.最后给出了应用计算结果 |
| 7. | Actually , this is to resolve an over - determined nonlinear system including six output values and eight input values . so newton - gauss iterative algorithms is used , set up the target function in the sense of the least squares . it is discussed whether the minimal solution to the function exist and is single one while the astringency of newton - gauss method is analyzed
对于冗余驱动振动台,其位姿正解是求解具有八个输入、六个输出的超定非线性方程组,因此本文采用了最小二乘法中的牛顿?高斯迭代法,建立最小二乘目标函数,对目标函数极小解的存在性、唯一性以及牛顿?高斯迭代法的收敛性进行了理论证明和分析,将求出的最小值作为位姿正解的最优解。 |
| 8. | Presents a method for sfs based on model of polyhedron . we carry out the algorithm by solving a overdetermined linear equations which is constructed through the distributing of the vector field . the algorithm can reconstruct 3d surface from photometric stereo image given the direction of illumination
针对目前“从明暗恢复物体形状方法”存在的问题，提出了以多面体模型为基础的快速算法，根据向量场的分布建立关于物体表面深度信息的超定线性方程组，在最小二乘意义下求得物体表面的深度值。 |
| 9. | In 1978 , professor zhang hong qing uses the method of gebraic elimination and factorization in differential equations and successfully solve a great kind of the reducing problem of the over determined differential equations . he gives the method of " ac = bd " which used to solve the differential equations . recently , this theories have a new development , and he forwards the c - d integrable system and c - d pairs
1978年，张鸿庆教授将代数消元和因式分解思想方法用于微分方程组，成功地解决了一大类超定微分方程组的约化问题，并提出解微分方程的“ ac = bd ”模式，近来这一理论又有了新的发展，提出了c ? d可积系统与c ? d对的概念。 |
