乘法

This paper presents a method of iteration for least absolute deviation regression,which uses weighted least squares methods.

利用加权最小二乘法，提出最小一乘的一种迭代算法，这种方法使最小一乘法在计算上变得简单、直

First, basing on point halving, this thesis proposed a new efficient algorithm of computing kP lQ on an elliptic curve over the finite field with characteristic 2 and analyzed the computational efficiency. When the ratio I/M of inversion to multiplication cost is small, this new algorithm is about 5%～30% faster than the traditional algorithms.

首先，基于半点运算给出一种计算特征为2的有限域上椭圆曲线双标量乘法kP lQ的新算法并分析了效率，当基域上求乘法与求逆的运算时间的比值比较小时，新算法的效率比已有算法提高5％～30％。

To raise the efficiency of scalar multiplication on elliptic curve,a scalar multiplication algorithm based on double base number system over binary field was improved.

为了提高椭圆曲线标量乘法效率，对二元域上椭圆曲线的基于双基数的标量乘法进行改进。

The concepts of weighted α-lower product and weighted α-upper product between a relation matrix and a Boolean column vector are presented in weighted approximation space.

在加权近似空间中提出了关系矩阵和布尔列向量加权α下乘法和加权α上乘法的概念。

Based on the point that there is something in common between the rules of matrix multiplication and the figure connection in braid multiplication, this paper gave a new representation of braid group called node matrix representation.

利用矩阵乘法规则与辫子乘法中图形的上下对应连接有类似之处这一特点，提出一种用结点矩阵表示辫子的方法。

The improved multiplication algorithm, can be a sign five multiplication, just change a few numbers can be easily extended to more digits multiplication process.

详细说明：采用改进的乘法算法，可进行有符号5位乘法运算，只需更改几个数字便可轻松扩展成更多位数乘法运算程序。

Finite Multiplicative Group In cryptography, we often use the multiplicative finite group: G = in which the operation is multiplication.

有限乘法群在密码学中，我们经常运用乘法有限群：G =，其中的运算是乘法。

And the Montgomery method to realize point multiplication is also efficient by using projective coordinates to reduce the multiplication times and only one time of inversion been needed.

利用Fermatt小定理求逆，根据有限域上元素的乘法满足结合律和交换律，通过重新安排乘法和平方的顺序，可以减少乘法和平方的次数，比按照定义直接实现速度提高了6倍。

It holds for the integers with addition and multiplication, but it does not hold for matrix multiplication or quaternion multiplication .

它所拥有的整数加法和乘法的，但是它并不拥有的矩阵乘法或四元数乘法。

With addition and multiplication defined componentwise, both R and R{D, C} are rings.Its clear that R is a subring of ?

R中加法和乘法分别定义为对应分量的加法与乘法，则R关于所定义的加法与乘法构成一个环，显然是？

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。