查询词典 triangular factorization

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。

They could be solved speedily by means of the sparse technique based triangular factorization.

应用稀疏矩阵的三角分解技术可实现对它们的快速求解。

In §5, we research a new fast triangular factorization algorithm of Hankel matrix. Then we give a numerical example.

在§5中，推导了Hankel矩阵的新的快速三角分解算法，给出了数值算例。

After the setup of a table of the spectral factorization results of each array of matrix, the SF decomposition can give the lower triangular matrix by reading the table.

特别是在复杂介质的偏移计算中，分解误差随介质的不均匀性程度的增大而增大，严重影响着波场的计算。

To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path.

使用对称矩阵的稳定Bunch-Parlett易于形成信赖域子问题的弧线路径，使用单位下三角矩阵作为最优路径和修正梯度路径的预条件因子。

By using the Cholesky factorization and inverse method for unit lower triangular matrix, the multi-sensor measurements with correlated measurement noises are transformed to equivalent pseudo ones with uncorrelated measurement noises; then based on the Kalman filtering, a new multi-sensor fusion target tracking algorithm with correlated measurement noises is proposed.

对于量测噪声相关的多传感器量测，利用Cholesky分解和单位下三角阵的求逆方法，将其转化为量测噪声互不相关的等价的多传感器伪量测，然后基于Kalman滤波，提出了一种解决量测噪声相关情况下多传感器融合目标跟踪问题的新算法。

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

The first is how to determine boundary curve of surface in triangular domain and after deducing, simultaneous equations is proposed in the dissertation. The second is how to determine the coupling parameter. The third is present simultaneous equations in order to obtain G1 continuous considering the continuity between two triangular patches and the fitness rules.

具体的工作体现在三个方面：一是对拟合条件下的三角域曲面边界线的确定，本文经过推演给出了求解方程组；二是对耦合参数的确定；三是在考虑相邻两片三角域曲面连续性的同时将拟合的规则纳入，给出了求解方程组以达到G 1连续。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

Margin of leaf blade crenate; petals triangular or triangular-ovate, apex obtuse, rarely acute.

叶片的边缘具圆齿；花瓣三角形的或三角状卵形，先端钝，很少锐尖。

A backer of an Afghan law that critics say legalizes marital rape has rejected the international outcry as foreign meddling.

饱受批评的一项法律的拥护者说合法化的婚内暴力不会受国际舆论的干涉。

Years ago, a ancient Egyptian fleet went to the Land of punt for seeking a kind of flavor named "myrrh", and aromatic plants which has dense exotic style for the queen Hatshepsut.

3500年前的一个古埃及的舰队到&彭特之地&寻找一种叫没药的香料。