| Multivariate Vandermonde Determinants and General Birkhoff Interpolation |
| |
| 作者姓名： | 朱平 |
| |
| 作者单位： | Multimedia Technology Institute, Xidian University, Xi＇an, 710071 |
| |
| 摘 要： | In this paper, we consider the Straight Line Type Node Configuration C (SLTNCC) in multivariate polynomial interpolation as the result of different kinds of transformations of lines (such as parallel translations, rotations). Corresponding to these transformations we define different kinds of interpolation problems for the SLTNCC. The expression of the confluent multivariate Vandermonde determinant of the coefficient matrix for each of these interpolation problems is obtained, and from this expression we conclude the related interpolation problem is unisolvent. Also, we give a kind of generalization of the SLTNCC in Section 5. As well, we obtain an expression of the interpolating polynomial for a kind of interpolation problem discussed in this paper.
|
| 关 键 词： | Vandermonde多变量行列式 多变量插值 Birkhoff插值 矩阵 SLTNCC |
Multivariate Vandermonde Determinants and General Birkhoff Interpolation |
| |
| ZHU Ping.Multivariate Vandermonde Determinants and General Birkhoff Interpolation[J].Northeastern Mathematical Journal,2005,21(3):336-344. |
| |
| Authors: | ZHU Ping |
| |
| Abstract: | In this paper, we consider the Straight Line Type Node Configuration C (SLTNCC) in multivariate polynomial interpolation as the result of different kinds of transformations of lines (such as parallel translations, rotations). Corresponding to these transformations we define different kinds of interpolation problems for the SLTNCC. The expression of the confluent multivariate Vandermonde determinant of the coefficient matrix for each of these interpolation problems is obtained, and from this expression we conclude the related interpolation problem is unisolvent. Also, we give a kind of generalization of the SLTNCC in Section 5. As well, we obtain an expression of the interpolating polynomial for a kind of interpolation problem discussed in this paper. |
| |
| Keywords: | multivariate Vandermonde determinant multivariate polynomial interpolation Birkhoff interpolation |
| 本文献已被 CNKI 维普 等数据库收录！ |
