阶乘的

First discarding the thought of fitting by AR model, the ARMA model is fitted by a high order MA model using Gevers-Wouters algorithm on the basis of related functions of ARMA model. Then according to the parameters of the fitted MA model, the ARMA model parameter estimation through solving a system of antipathic linear equations using the least squares method is obtained.

首先摈弃传统的拟合到AR模型的思考方法，而是基于ARMA模型的相关函数用Gevers-Wouters算法对ARMA模型拟合到高阶滑动平均模型；然后在拟合的MA模型参数基础上，用最小二乘算法求解一个不相容的线性方程组，从而估计出ARMA模型参数。

Then,a new fast algorithm of the minimal norm least squares solution for linear system whose coefficients is an m×n symmetric Loewner matrix with full column rank is given by forming a special block matrix and researching the triangular factorization of its inverse.

对于工程计算中常常遇到的一类线性方程组的求解，通过构造特殊分块矩阵并研究其逆矩阵的三角分解，给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组，及极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

A new fast algorithm of the minimal norm least squares solution for the linear system whose coefficient matrix is an m×n Loewner-type matrix with full column rank is given by forming a special block matrix and researching its triangular factorization.

通过构造特殊分块矩阵及其三角分解给出了求秩为n的m×n阶Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

In Chapter three, by constructing a special partitioned matrix and studying the fast triangular factorization of its inverse matrix, we respectively give fast algorithms for the minimal norm least squares solutions of linear equations which coefficient matrices are n×m Toeplitz type matrices and Vandermonde-Loewner type matrices with full column rank.

第三章通过构造特殊分块矩阵并研究其逆矩阵的快速三角分解，分别给出了求以秩为m的n×m阶Toeplitz型矩阵和Vandermonde-Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，并通过算例将新算法与已有的法方程组的方法和正交化方法作了比较。

Fast algorithm of minimal norm least square solution for Cauchy linear system;2. For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.

对于秩为n的m×n阶Cauchy型矩阵C，通过构造特殊分块矩阵并研究其三角分解，进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法，所需运算量为O+O(n2)，而通常构造法方程组的方法所需运算量为O(m n2)+O(n3)，用正交化法虽然避免了构造法方程组，但所需的运算量更大些。

Since the B-spline is a locally supported function, the smoothing formula can be strictly limited in a neighborhood of each point. The smoothing surface defined by the smoothing formula has the same convexity as that of the original image. Secondly, the edge points are detected by either computing the local extremum points of the directional derivative or computing zero-crossing of the second-order directional derivative of the smoothing surface. Finally, an example of an edge detector is given.

针对反卷积视觉模型的病态性，增加了适当的约束，给出了基于低松弛迭代格式的快速自适应滤波算法，对于一个N×N输入图象，由于变换核的局部支撑性质以及低松弛迭代格式的引入，使得快速自适应滤波算法的计算复杂度降为象素个数N〓的线性量阶N〓，就最小二乘算法的复杂性而言，优于不动点迭代算法的O以及基于FFT的预处理共轭梯度算法的O。

Although the merit function introduced here is the sum of squares of overdetermined equations, by using the special structure of it, we successfully form the Newton equation by avoiding the product of Jacobi matrices and using only the Jacobi matrix of the function defining NCP.

对非线性互补问题，利用所构造价值函数具有的特殊非线性最小二乘结构，成功实现了具有一般意义的构造Newton方程时仅利用价值函数的一阶导数且无须计算相应残量函数Jacobi矩阵乘积的Newton法。

The integral steering vector of coherently distributed source is deduced to be a Schur-Hadamard product comprising the steering vector of the point source and a real vector. And then a second statistics is proposed for the data collected at subarray X, the rotational invariance matrices can be estimated based on propagator method.

该算法通过将积分形式的相干分布式信源方向向量化简为点信源方向向量与实向量的Schur-Hadamard积，对子阵X接收的数据构造二阶统计量；利用传播因子最小二乘估计子阵X与Z，X与W之间的旋转不变矩阵。

Then the generalized moving least squares approximation is derived under adding the residual of high orders derivative.

从而，进一步导出了不仅要求近似函数还要求其任意阶导数在各节点处的误差的平方和最小的广义移动最小二乘近似。

In this paper ,we present a class of new factorized quasi-Newton algorithms for nonlinear least squares problems which are based on new quasi-Newton equation and factorized quasi-Newton method.

本文根据具有更高的二阶曲率逼近的新拟牛顿方程，结合针对非线性最小二乘问题特点的分解式算法，提出了基于新拟牛顿方程的分解拟牛顿算法。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。