摘要
在多元向量值分叉连分式的构造中,特征问题的讨论尤为重要,结果已经给出了n元向量值分叉连分式插值的特征猜想,即一个n维插值点集包含N个元素,则建立在该点集上的n元向量值插值连分式将是一个分子为N-1次,分母为2[(N-1)/2]次的向量值有理函数,该文证明了这一猜想。
The characterization issue is of especial significance in the construction of the multi-variable branched vector-based continued fractions. In the related literature, an conjecture has been put forward that if an n-dimensional set of points, Ⅱ, contains N elements, then a vector valued continued fraction with n entrances of branches can be constructed and it is a vector valued rational function in Rn with total degrees of the numerator and denominator reaching N-1 and 2[ （N-1）/2] respectively. In this paper, the conjecture is proved.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第10期1371-1375,共5页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(10171026
60473114)
安徽省自然科学基金资助项目(070416273x)
安徽省教育厅科技创新团队基金资助项目(2005TD03)
关键词
向量值
分又连分式
特征定理
vector value
branched continued fraction
characterization theorem
