摘要
Mathar讨论了在范数‖·‖_p^(s)下距离矩阵的最佳欧氏逼近问题。本文把这一结果推广到范数‖·‖_u^(s),这里‖·‖_u是任意正交不变范数,并指明对任意的s,E_n总提供最佳欧氏逼近。控制不等式和对称标尺函数在本文起基本的作用。
Mathar's results about the best Euclidian fit to a given distance matrix in prescribed dimension under norm‖·‖_p^(s) are extended to norm ‖·‖_u^(s), where ‖·‖_u is an arbitrary orthogonal invariant norm, and it is showed that E_n gives the best Euclidian fit for any s. Majorization inequalities and symmetric gauge functions serve as basic tools.
出处
《北京师范大学学报（自然科学版）》
CAS
1987年第4期21-24,共4页
Journal of Beijing Normal University(Natural Science)
关键词
距离矩阵
最佳欧氏逼近
distance metrix, the best Euclidian fit.
