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In this paper, for m× n Loewner-type matrix or symmetric Loewner-type matrix with full column rank, we form special block matrix firstly and research their triangular factorization or of its inverse, and then get the fast algorithm of the minimal norm least squaresolution .

本文对于秩为n的m×n阶Loewner型或对称Loewner型矩阵L，通过构造特殊分块矩阵并研究其逆的三角分解或自身三角分解，进而得到了线性方程组Lx=b的极小范数最小二乘解快速算法，计算复杂度为O+O(n~2)，而一般方法的计算复杂度为O(mn~2)+O(n~3)。

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。

In United States, newspaper advertisement still use this as a unit to calculate column space, i.e. number of Agate lines of a certain column width.

在美国，报纸上的广告仍用这个单位计算篇幅，即若干雅基行乘柱位阔。

Particularly, when the dimension of input space of the column reduced interval polynomial fraction model is one, the result can be reduced to the well-known Box theorem in robust control.

为了使这种模型更接近于实际系统，文中分别采用了范数有界的加性扰动和乘性扰动以及Gap度量来反映系统的非结构扰动部分。

A column vector, that is one whose components are written as a column and treated as a k by 1 matrix.

行向量，其物件排列成行，可视为k乘1的矩阵。

American comedist Si Keer pauses (was born 1913) go to Europe going sightseeing by plane with a few his friends, he himself still will go out in London Pallas theater act.

1951年，美国喜剧作家斯克尔顿（1913年出生）和他的几个朋友乘飞机去欧洲观光，他本人还将在伦敦雅典娜剧院出演。

Seat of automobile is the interface people contact with the automobile, people's driving comfortableness by car relates to seat mainly.

汽车中的座椅是人与汽车接触的界面，人们驾乘汽车的舒适性主要与座椅有关。

Commendatore Beninobenone having been extricated from underneath the presidential armchair, it was explained by his legal adviser Avvocato Pagamimi that the various articles secreted in his thirtytwo pockets had been abstracted by him during the affray from the pockets of his junior colleagues in the hope of bringing them to their senses.

人人欢迎九尺汉子这个随机应变的建议，全场一致通过。绿宝石岛之友个个都向麦克法登巡警衷心表示谢忱，而其中几个正大量淌着血。骑士团司令官贝尼诺贝诺内被人从大会主席的扶手椅底下解救出来，然后他的法律顾问帕格米米律师解释说，藏在他那三十二个兜里的形形色色的物品，都是他乘乱从资历较浅的同僚兜里掏出来的，以促使他们恢复理智。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！