| THE NOTE ON MATRIX-VALUED RATIONAL INTERPOLATION |
| |
| 作者姓名： | 朱晓临 朱功勤 |
| |
| 作者单位： | Department of Mathematics, Hefei University of Technology, Hefei 230009,PRC. |
| |
| 基金项目： | Supported by the National Natural Science Foundation of China （10171026 and 60473114）. |
| |
| 摘 要： | In 3], a kind of matrix-valued rational interpolants （MRIs） in the form of Rn（x） = M（x）/D（x） with the divisibility condition D（x） ｜ ｜｜M（x）｜｜^2, was defined, and the characterization theorem and uniqueness theorem for MRIs were proved. However this divisibility condition is found not necessary in some cases. In this paper, we re- move this restricted condition, define the generalized matrix-valued rational interpolants （GMRIs） and establish the characterization theorem and uniqueness theorem for GMRIs. One can see that the characterization theorem and uniqueness theorem for MRIs are the special cases of those for GMRIs. Moreover, by defining a kind of inner product, we succeed in unifying the Samelson inverses for a vector and a matrix.
|
| 关 键 词： | 矩阵值 有理数插值 唯一性 可分割条件 |
| 收稿时间： | 2002-12-21 |
THE NOTE ON MATRIX-VALUED RATIONAL INTERPOLATION |
| |
| Zhu Xiaolin,Zhu Gongqin.THE NOTE ON MATRIX-VALUED RATIONAL INTERPOLATION[J].Numerical Mathematics A Journal of Chinese Universities English Series,2005,14(4):305-314. |
| |
| Authors: | Zhu Xiaolin Zhu Gongqin |
| |
| Abstract: | In 3], a kind of matrix-valued rational interpolants (MRIs) in the form of Rn(x) = M(x)/D(x) with the divisibility condition D(x) | ‖M(x)‖2, was defined, and the characterization theorem and uniqueness theorem for MRIs were proved. However this divisibility condition is found not necessary in some cases. In this paper, we remove this restricted condition, define the generalized matrix-valued rational interpolants (GMRIs) and establish the characterization theorem and uniqueness theorem for GMRIs. One can see that the characterization theorem and uniqueness theorem for MRIs are the special cases of those for GMRIs. Moreover, by defining a kind of inner product,we succeed in unifying the Samelson inverses for a vector and a matrix. |
| |
| Keywords: | generalized matrix-valued rational interpolants reduced matrix-valuedrational interpolants uniqueness |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
