低维空间上分片线性函数的逼近因子与剖分数  

Approximation factors and subdivision s number of piecewise linear functions in low dimensional space

作　　者：陶玉杰 由巧俐[2] 李晓萍[3] TAO YU-jie;YOU Qiao-li;LI Xiao-ping(School of Mathematics,Tonghua Normal University,Tonghua 134002,China;Department of Mathematics,Teacher s College,Easten Liaoning University,Dandong 118003,China;School of Management,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]通化师范学院数学学院,吉林通化134002 [2]辽东学院师范学院数学系,辽宁丹东118003 [3]天津师范大学管理学院,天津300387

出　　处：《东北师大学报（自然科学版）》2021年第2期19-24,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61374009);吉林省教育厅科学技术研究项目(JJKH20210540KJ).

摘　　要：引入了分片线性函数及矩阵行列式的解析表示,通过低维欧氏空间几何模型和等距剖分提出逼近因子的概念,并基于差值因式给出对应矩阵行列式的代数余子式和矩阵模的计算方法.依次证明了输入空间的剖分数与1元、2元和3元分片线性函数的逼近因子均无关,但剖分数与分片线性函数及其逼近精度却有关.The concepts of multivariate piecewise linear function and the matrix determinant representation are first introduced.The definition of approximation factor is introduced by geometric model of low dimensional Euclidean space and isometric subdivision,and a calculating method of the algebraic cofactor and matrix norm for the corresponding determinant is given based on the difference factor.Finally,it is proved that the approximation factors of the piecewise linear functions of unary,binary and ternary are constants independent of the subdivision s number,but the subdivision s number is related to the piecewise linear function and its approximation accuracy.

关 键 词：分片线性函数 剖分数 矩阵行列式 代数余子式 矩阵模 逼近因子 

分 类 号：O159[理学—数学]