托普勒兹矩阵和广义托普勒兹矩阵的分解

给出了广义托普勒兹矩阵的生成多项式和分解多项式的概念；借助于多项式理论证明了复数域上任意一个n阶托普勒兹矩阵和广义普勒兹矩阵都可分解为n个托普勒兹块阵的乘积。     

Smooth interpolation on homogeneous matrix groups for computer animation

INTRODUCTION Homogeneous matrices are matrices used to represent geometric transformations for homogene- ous coordinates. Because they provide uniform rep- resentation for various transformations, they are widely used in the computer graphics community. As a homogeneous matrix corresponds to a geometric transformation, a curve on the set of homogeneous matrices can be taken as a piece of motion. Thus interpolation between those matrices is of high in- terest in many applications such as c…     

一类图的伴随多项式的因式分解及色性分析

我们通过研究图的伴随多项式的因式分解，得到了一类图的色等价图的结构特征．     

大整数的阶乘运算

利用百进制,本文提出一种整数阶乘精确的计算及其结果输出的方法.通过进制的增大可处理更大整数的阶乘.     

几类特殊r-循环阵的逆

本文利用多项式理论给出了几类特殊r-循环阵逆阵的求法.     

基于一个新核函数的半定规划的内点算法的复杂性分析

Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.     

矩阵多项式的求逆

本文对矩阵多项式的求逆给出了一般方法,并针对于每一种方法给出了具体实例.     

多项式向量场空间的维数与基

本文借助于数域P上的n次多项式的齐次分解,证明了线性空间P[X1,X2,…Xn]m的维数等于Cn＋m^n并给出了该空间的一组基;进而得到R^n上次数不超过m的多项式向量场的全体构成的线性空间V的维数等于n·Cn＋m^n。     

关于一个广义Euler多项式的恒等式

用初等的方法研究了一个广义Euler多项式的性质,并得到了一组恒等式.     

Least-squares function-valued Padé-type approximation and its application in solving integral equations

To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.