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normal equation
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  法方程
    Nonsingularity of coefficient matrix of normal equation in least-square estimator of non-linear semiparametric models
    非线性半参数模型最小二乘核估计法方程系数阵的非奇异性质
短句来源
    In this paper, after analysing the normal equation method for weighted least square (WLS) state estimation in power system and pointing out the potential problem of this method in numerical stability, a fast orthogonal transformation algorithm which uses fast Givens transformation to solve WLS state estimation is presented.
    本文分析了电力系统加权最小二乘状态估计(Weighted Least Square=WLS)法方程算法潜在的数值稳定性问题,提出了用正交变换(二乘Givens变换)解WLS状态估计的快速正交变换算法。
短句来源
    This paper presents computer general expressions which include: (1) calculation of the coefficient of normal equation;
    本文提供的电算通式有:(1)法方程系数的计算;
短句来源
    The resolution to the normal equation of variational inequality problem
    变分不等式问题的法方程解法
短句来源
    In this thesis, iterative method associatedwith the normal equation is used to find the problems centrosymmetric least-squares solutions, centroskew symmetric least-squares solutions, re?
    本文利用迭代法结合法方程变换的方法来求大型线性矩阵方程AX = B的中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反矩阵、对称正交对称、对称正交反对称最小二乘解,同样也成功地解决了这些问题.
短句来源
更多       
  正规方程
    The Other Form of Regression Coefficient Covariance Matrix of a Normal Equation
    正规方程另一形式的回归系数协方差矩阵
短句来源
    Acquires the least squares solutions of the matrix equation AXB=E,CXD=F by constructing the normal equation of the matrix equation and applying the generalized singular-value decomposition of coefficient matrices.
    借助于矩阵方程AXB=E,CXD=F的正规方程及系数矩阵的广义奇异值分解,得到了此矩阵方程的最小二乘解。
短句来源
    Generally, a linear least squares problem leads to ihc solution of the so called normal equation.
    解线性最小二乘问题时,通常都要解所谓正规方程.
短句来源
    Power system state estimation is usually formulated as a weighted least-squares problem and is solved iteratively by the normal equation method.
    电力系统加权最小二乘准则的状态估计,通常采用正规方程法。
短句来源
  正规方程
    The Other Form of Regression Coefficient Covariance Matrix of a Normal Equation
    正规方程另一形式的回归系数协方差矩阵
短句来源
    Acquires the least squares solutions of the matrix equation AXB=E,CXD=F by constructing the normal equation of the matrix equation and applying the generalized singular-value decomposition of coefficient matrices.
    借助于矩阵方程AXB=E,CXD=F的正规方程及系数矩阵的广义奇异值分解,得到了此矩阵方程的最小二乘解。
短句来源
    Generally, a linear least squares problem leads to ihc solution of the so called normal equation.
    解线性最小二乘问题时,通常都要解所谓正规方程.
短句来源
    Power system state estimation is usually formulated as a weighted least-squares problem and is solved iteratively by the normal equation method.
    电力系统加权最小二乘准则的状态估计,通常采用正规方程法。
短句来源
  “normal equation”译为未确定词的双语例句
    A minimizing algorithm of solving large-scale sparse normal equation
    大型稀疏法方程组极优化分解算法
短句来源
    This paper studies the relation between the residuals of GCR algorithm and the spectral distribution bound of coefficient matrix. It is analyzed thatthe practicability and limitation of GCR algorithm and the rough criterion is gived. It is compared with GCR algorithm that using conjugate gradient methodto solving the normal equation.
    本文探讨了GCR算法的残量与系数阵谱分布界间的关系,分析了其局限性及可行性,给出了粗略的判别标准,并与古典的共轭斜量法解法方程组的方法作了比较。
短句来源
    In order to avoid the computational error introduced by direct constructing normal equation group, the algorithms can be divided into two classes. One is Gram Schmidt or covariance matrix method, in which we transform the base function set to meliorate the condition of the normal equation group.
    为避免因直接构造法方程组而引入计算误差,这些方法归结为两种思路:一是从基底函数系入手,通过变换函数族的基底来改善法方程组状态;
短句来源
    There are two topics that will be noticed when utilizing the Uniform Design: 1. In the tables of Uniform Design, there are several experiment planes that have column linear equivalent phenomena. When proceeding regression analysis on the result of the experiments, the normal equation group is ill conditioned and will gain an imperceptible false conclusion.
    使用均匀设计试验时有两点须要注意的问题 :1 .均匀设计表中有若干个试验方案有列共线现象 ,对其试验结果进行回归分析时 ,正则方程组是病态的 ,将得到不易察觉的错误结论 ;
短句来源

 

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      normal equation
    The primal direction requires solving a least squares problem whose normal equation matrix is composed of a block-Toeplitz portion plus other structured matrices.
          
    In the case of the core solver, it is demonstrated that the assembling and rigorous solution of large normal equation systems can be handled by using Beowulf clusters within a reasonable computing time.
          
    the rigorous solution of the corresponding large normal equation systems applying parallel processing (on a PC cluster) as the core solver, and the fast semianalytic approach as a quick-look gravity field analysis (QL-GFA) tool, is proposed.
          
    Their computation leads to the solution of very large normal equation systems.
          
    The traditional observation and normal equation matrices are substituted by partial differential equations with corresponding boundary conditions.
          
    更多          


    In this paper a normal equation is derived for orthogonal gridworks loaded normally to their planes analyzed by the slope-deflection-gyration method.

    本文把一般结构力学的用变形法计算平面刚架的原理应用到交叉梁系上,得到了一组法方程式,考虑了扭矩的影响。

    This paper deals with the applioations of multiple-knot cardinal δ-spline function interpolation to the problem of fitting in a great deal data, as a continuation to past(Ⅰ) and(Ⅱ)of the same title by the same author.The author has established the least squares fit by multiple-knot δ-spline, pointed out that coefficient matrix of the system of its normal equation has the characteristics of band and majorant and so on,and estimated its condition number for degree of m.c.δ-spline k≤3.The given intrisical...

    This paper deals with the applioations of multiple-knot cardinal δ-spline function interpolation to the problem of fitting in a great deal data, as a continuation to past(Ⅰ) and(Ⅱ)of the same title by the same author.The author has established the least squares fit by multiple-knot δ-spline, pointed out that coefficient matrix of the system of its normal equation has the characteristics of band and majorant and so on,and estimated its condition number for degree of m.c.δ-spline k≤3.The given intrisical property and its explicit expression would bring facilities for its applications, especially for computer-aided geometricdesign.

    本文研究多结点基数型δ-spline函数对大量数据拟合问题的应用,是同名文章(Ⅰ)、(Ⅱ)的继续。我们将给出多结点样条的最小二乘逼近方法,指出正规方程组的系数矩阵具有带状强对角优势等特点,并对实用的k=2,3的情形给出了条件数估计。 正规方程组的良好性质及逼近样条的显式表达将给它的应用,尤其是计算机辅助几何设计有关问题,带来极大的方便。

    The mathematical model of simulation test is a differential equation of order 6, with a non-linear oscillatory form as follows: dx/dt=A_1x+g_1(t,x) (1) In this paper we have proved the following theorems: Theorem 1. System(1) is "dissipative" (D-system).Consequently its solutions are uniformly ultimately bounded. Theorem 2. In system(1) there exists at least one harmonic solution. Theorem 3. Supposing that the system(1) has more than one harmonic solutions, then its parameters should satisfy the following condition:...

    The mathematical model of simulation test is a differential equation of order 6, with a non-linear oscillatory form as follows: dx/dt=A_1x+g_1(t,x) (1) In this paper we have proved the following theorems: Theorem 1. System(1) is "dissipative" (D-system).Consequently its solutions are uniformly ultimately bounded. Theorem 2. In system(1) there exists at least one harmonic solution. Theorem 3. Supposing that the system(1) has more than one harmonic solutions, then its parameters should satisfy the following condition: [-B~3/(8(1+ε)~3)]~2+[1/(54bβ)((27bβB~2)/((1+ε)~2)+24aβ-8(1+ε))]~3≤0 (2) Theorem 4. Supposing that the system(1) satisfies the following conditions: ①inequality(2) holds; ②there are n_1, Galerkin approximations (t) of order m, and the error η_1~(j)(t) of such a Galerkin approximation satisfies ||η_1~(j)(t)||≤r_2~(j), j=1,2,……n_1; ③there exists a positive numbers r~(j) such that the local Lipsehitz Constant L_r~(j) of the normal equation of system(1) in S_j:||y-φ~(j)||≤r~(j) and r~(j), r_2~(j) satisfies then in the system(l) there exist at least n, harmonic solutions which lie respectively in the neighborhood of Galerkin approximation ~(j)(t) of order m.

    模拟试验的数学模型是六阶非线性振动型微分方程,其等价形式为: dx╱dt=A_1x+g_1(t,x) (1) 本文证明了以下定理: 定理1.方程(1)属于“D类系统”,因而一切解均匀最终有界。定理2.方程(1)至少存在一个调和解。定理3.若方程(1)有多于一个的调和解,则其参数应满足: [(-B~3)╱(8(1+ε)~3)]~2+[1╱(54bβ)((27bβB~2)╱(1+ε)~2+24αβ-(8(1+ε)))]~3≤0 (2) 定理4.设方程(1)满足下列三个条件①不等式(2)成立; ②求得n_1个m阶Galerkin逼近~(j)(t),相应误差η_1~(j)(t)适合‖η_1~(j)(t)‖≤r_2~(j),j=1,2,……n_1; ③存在正数r~(j)使得(1)的典则化方程在S_j:‖y-φ~(j)‖≤r~(j)中的局部Lipschitz常数Lr~(j)以及r~(j),r_2~(j)满足(1+max|λi+k|)/(min|λi+k|)·(3r_2~(j))/(δ≤σ((σ-KLr~(j)))/(K~2Lr~(j)))r~(j)i=1,2,3,4, j=1,2,……n_1且S_i∩S_h=0 i≠h;...

    模拟试验的数学模型是六阶非线性振动型微分方程,其等价形式为: dx╱dt=A_1x+g_1(t,x) (1) 本文证明了以下定理: 定理1.方程(1)属于“D类系统”,因而一切解均匀最终有界。定理2.方程(1)至少存在一个调和解。定理3.若方程(1)有多于一个的调和解,则其参数应满足: [(-B~3)╱(8(1+ε)~3)]~2+[1╱(54bβ)((27bβB~2)╱(1+ε)~2+24αβ-(8(1+ε)))]~3≤0 (2) 定理4.设方程(1)满足下列三个条件①不等式(2)成立; ②求得n_1个m阶Galerkin逼近~(j)(t),相应误差η_1~(j)(t)适合‖η_1~(j)(t)‖≤r_2~(j),j=1,2,……n_1; ③存在正数r~(j)使得(1)的典则化方程在S_j:‖y-φ~(j)‖≤r~(j)中的局部Lipschitz常数Lr~(j)以及r~(j),r_2~(j)满足(1+max|λi+k|)/(min|λi+k|)·(3r_2~(j))/(δ≤σ((σ-KLr~(j)))/(K~2Lr~(j)))r~(j)i=1,2,3,4, j=1,2,……n_1且S_i∩S_h=0 i≠h;则方程(1)至少存在n_1个调和解,它们分别出现在m阶Galerkin逼近~(j)(t)的附近。

     
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