张量分解在齐次多项式中的应用  

Applications of Tensor Decomposition in Homogeneous Polynomials

作　　者：潘珺珺[1] 卢琳璋[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2015年第3期347-350,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11261012)

摘　　要：针对n元m次齐次实系数多项式,提出了对应的m阶n维系数张量的定义,并应用张量分解,给出了该类多项式因子分解的充要条件.证明了该类多项式总是可以写成若干个因式之和,因此通过构造系数张量就能得到所需要的因式之和.We consider n-variable homogeneous polynomials of degree m with real coefficients.We propose the corresponding coefficient tensors of order mand n-dimension.A necessary and sufficient condition for the polynomial factorization isgiven by using tensor decomposition to its coefficient tensor.We prove that the polynomial can be written as a sum of factors.Therefore,we can obtain the sum we desire by reconstructing its coefficient tensor.

关 键 词：齐次多项式 张量 TT格式 

分 类 号：O151.23[理学—数学]