查询词典 factorization

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。

In this paper, firstly the elimination tree theory is introduced in brief, and the structure of Jacobian matrix is determined by use of symbolic factorization; then by use of sparse vector method each column of lower triangular matrix L and each row of upper triangular matrix U are solved.

介绍了消去树理论，并采用符号因子分解技术确定雅可比矩阵的结构，然后采用稀疏向量法求取L阵的每行和U阵的每列。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

It is based on the difficulty of computing the discrete logarithm modulo for a composite number and the factorization problem of large integer.The size of the group signature and verification time of the group signature are equivalent to that of an individual signature.

该方案的安全性是基于求离散对数和RSA大整数因式分解的困难，其群签名长度和群签名的验证时间只相当于一般个人签名。

Uenced by lighting, expres-sion, view, and age, we apply tensor factorization to extracting multi-factor representationfor faces and propose a TF-based model for facial view estimation and an algorithm with themeasure of correlation between tensor representation and view factor.

考虑到人脸图像受光照、表情、视角、年龄等多种因素的影响，我们用张量分解方法同时提取人脸图像中的多因子表征，进而构建一个基于张量分解的人脸视角感知模型。

This paper discusses the relation beween order classification and isomorphic classification , gives some important characteristic properties of a cyclic group with order n and a important property of a p-group with finite order, introduces two factorization method of direct product for commutative p-group with finite order, presents some new problems.

讨论了阶分类与同构分类的关系，给出了n阶循环群的几个重要的特征性质和有限p-群的一个重要性质，介绍了有限交换p-群直积分解的两种方法，提出了一些新的问题。

By using the group-chain, the wavefunctions of the 4f〓 configuration for RE ions are also expressed as linear combinations of group-chain basis functions in Butler's irreducible representation notation. The matrix elements of the CF Hamiltonian then are calculated by means of the Wigner-Eckart theorem and factorization lemma of the jm factors. Before the CF level fitting, a point-charge calculation of the conventional CF parameters B〓 has been performed by means of the lattice-sum technique from the known crystal structure data. The corresponding parameters in the group-chain are calculated by the conversion relationship between two schemes that proved identical in essence, which are usually used as initial values in the fit to the experimental levels. The ratios of the same k-value CF parameters are suggested as the constraint conditions in the fit, in order to utilize fully the symmetry distortion degree of the studied system.

利用群链理论，属稀土离子4f〓组态的波函数表示为以不可约表示标记的群链基波函数的线性组合；借助Wigner-Eckart定理和2jm和3jm因子的分解定律计算了晶场哈密顿的矩阵元；根据点电荷模型和已知晶体结构数据，利用点阵求和技术计算得到传统晶场参数B〓初值，相应的非传统形式的群链参数初值则由两种方案下的转换关系求得；这些初值通常作为非线性拟合晶场能级计算的初值，系统的对称性畸变信息则反映在以同阶晶场参数的比值作为能级拟合的约束条件。

To get high numerical stability and computational efficiency, U-D factorization-based DFP and BFGS algorithms are developed.

该算法解决了H阵的正定性问题，保证了算法的数值稳定性，并大大提高了计算效率。

Two forms of implicit TVD schemes are proposed in this paper for the simulation of nonequilibrium flows past hypersonic re entry vehicle, which are derived from the diagonal form of an approximate factorization algorithm and lower upper scheme applied to the implicit part of Harten Yee's TVD scheme respectively.

针对高超音速化学非平衡流提出了两种隐式格式。一种是近似因子分解算法对角化形式在隐式TVD格式上的推广，另一种可视为隐式TVD格式的LU分解形式。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。