乘法的

By using the principle of least absolute deviation method , we will give a new priority method—least logarithm absolute deviation method.

利用最小一乘法原理，在层次分析中提出了一种新的排序方法——对数最小一乘法，并将其转化成线性规划问题求解，证明了对数最小一乘法的一些性质。

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。

Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.

本文首先介绍了椭圆曲线密码的有关基本概念；其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算，对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析，给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法，并对IEEE P1363 标准给出的标量乘法做了改进，使得标量乘法的运算效率提高了近10%；最后介绍了利用复乘计算标量乘法的方法，对已有的方法进行总结归纳，得出完整的计算过程，并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法，得出一类普遍的结果，并给出了进一步用复乘加快标量乘法的思路。

The basic principle of least-squares method is to choose the model parameters minimizing model error sum of squares, thus the name "least squares method."

最小二乘法的基本原理是选择模型参数极小化模型误差平方和，因此而得名"最小二乘法"。

In this paper, introduces firstly a concept of polynomial coefficient matrix, and then the polynomial multiplication is masterly changed into the computing of matrix multiplication. Then a theorem is received. Throughout the process, the steps are very clear and the calculating is pretty simple.

该文首先引进了一个多项式系数矩阵的概念，然后巧妙地将多项式的乘法转变为矩阵乘法的运算，得到了一个定理，步骤清晰，计算简单。

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。

In chapter two, the fast implementation problems of the elliptic curve cryptosystems are studied. In this chapter, the problems are firstly reduced to the computations of the scalar multiplication of the elliptic curves.

第二章首先通过研究各种椭圆曲线密码体制，将椭圆曲线密码的快速实现问题归结为对标量乘法的计算，然后简单概述了标量乘法快速运算的一般算法。

A field inversion is the most expensive operation on scalar multiplication, and the number of inversion determines the performance of scalar multiplication.

求逆是标量乘法中最耗时的运算，求逆运算次数的多少直接决定标量乘法的性能。

In the second chapter, we present the traditional way of surface fitting ------LeastSquares. We present a kind of amendatory algorithm------Moving Least Squaresbased on Least Squares.

第二章介绍曲面拟合的传统方法——最小二乘法的理论，在此基础上，采用了一种改进的曲面拟合方法——移动最小二乘法。

Preparation of high-performance Stranssen matrix mult...

++编写的高性能矩阵乘法的Stranssen算法，能够有效提高矩阵乘法的效率。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了