| 向量值有理插值存在性的一种判别方法 |
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| 引用本文： | 刘智秉,朱功勤.向量值有理插值存在性的一种判别方法[J].大学数学,2004,20(6):50-54. |
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| 作者姓名： | 刘智秉 朱功勤 |
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| 作者单位： | 合肥工业大学,理学院,安徽,合肥,230009;合肥工业大学,理学院,安徽,合肥,230009 |
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| 摘 要： | 对于向量值有理插值的计算,目前已经有多种求解算法.但其存在性的判别方法及其证明在现有的文献中还没有见到.这里利用标量有理插值函数插值存在性的思想,引入Newton基函数,给出并证明了向量值有理插值存在性的一种判别方法.同时给出有理插值函数的分子和分母的显式表达式,最后的实例说明了它的有效性.
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| 关 键 词： | 向量值有理插值 向量值连分式 Newton基函数 充要条件 |
| 文章编号： | 1672-1454(2004)06-0050-05 |
| 修稿时间： | 2003年10月13 |
A Decision Method for Existence of Vector-Valued Rational Interpolants |
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| LIU Zhi-bing,ZHU Gong-qin.A Decision Method for Existence of Vector-Valued Rational Interpolants[J].College Mathematics,2004,20(6):50-54. |
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| Authors: | LIU Zhi-bing ZHU Gong-qin |
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| Abstract: | There are many algorithms for vector-valued rational interpolants, but the decision method as well as prove of its existence have not been seen in existing papers. In this paper, a decision method as well as the proof for existence of vector-valued rational interpolants are given, and the expression of the rational interpolants' numerator and denominator are given. In the end, its validity is proved by examples. |
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| Keywords: | vector-valued rational interpolants vector-valued continued fractions Newton basic function necessary and sufficient conditions |
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