| 判别有理插值函数存在性的一种新方法 |
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| 引用本文： | 荆科,王茂华. 判别有理插值函数存在性的一种新方法[J]. 阜阳师范学院学报(自然科学版), 2014, 0(2): 6-8 |
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| 作者姓名： | 荆科 王茂华 |
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| 作者单位： | 阜阳师范学院数学与金融学院,安徽阜阳236037 |
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| 基金项目： | 基金项目：安徽省自然科学基金项目（1408085MD70）;国家特色专业（数学与应用数学TS11496）;安徽省高校省级自然科学研究项目（KJ20132268）;阜阳师范学院科研项目（2013FSKJ11）资助. |
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| 摘 要： | 有理插值函数的存在性问题是有理插值研究的一个重要内容。现有的关于有理插值函数的存在性的方法都是基于求解齐次线性方程组的方法,其系数矩阵的阶数较高,计算复杂度较大。本文利用牛顿差商的性质和分段组合的方法,给出了一种判别有理插值函数存在的方法。较之其他方法,具有计算复杂度较小、承袭性等优点。
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| 关 键 词： | 有理插值 牛顿差商 分段组合 承袭性 齐次线性方程组 |
A new criterion for the existence of the rational interpolation functions |
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| JING Ke,WANG Mao-hua. A new criterion for the existence of the rational interpolation functions[J]. Journal of Fuyang Teachers College:Natural Science, 2014, 0(2): 6-8 |
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| Authors: | JING Ke WANG Mao-hua |
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| Affiliation: | (School of Mathematics and Finance, Fuyang Teachers College, Fuyang Anhui 236037, China) |
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| Abstract: | The existence of rational interpolation function is an important field in the study of rational interpolation. Existing methods about the existence of rational interpolation function are based on the method of solving the homogeneous linear equations, which has the high order matrix and the high complexity of computation. In this paper, by use of the properties of Newton difference quotient and the method of piecewise combination, we present a method to judge the existence of rational interpolation function. Compared with other methods, it has the advantages of heredity and low complexity of computation. |
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| Keywords: | rational interpolation Newton difference quotient piecewise combination heredity homogeneous linear equations |
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