| 三元Thiele-Newton型有理插值 |
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| 引用本文： | 王家正. 三元Thiele-Newton型有理插值[J]. 河南科技大学学报(自然科学版), 2006, 27(6): 83-86 |
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| 作者姓名： | 王家正 |
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| 作者单位： | 安徽教育学院,数学系,安徽,合肥,230061 |
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| 基金项目： | 安徽省教育厅自然科学基金项目（2005KJ211） |
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| 摘 要： | 将Th iele型插值连分式与二元Newton插值多项式结合起来构造三元有理函数,通过引入三元混合差商和倒差商建立了三元有理插值的递推算法、特征定理,给出了相应的证明,并通过数值例子验证了算法的有效性。三元有理插值在几何造型、图像处理、计算机辅助设计等领域都有直接的应用。
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| 关 键 词： | 连分式 有理插值 倒差商 特征定理 |
| 文章编号： | 1672-6871（2006）06-0083-04 |
| 收稿时间： | 2006-04-10 |
| 修稿时间： | 2006-04-10 |
Tri-variate Thiele-Newton''''s Rational Interpolants |
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| WANG Jia-Zheng. Tri-variate Thiele-Newton''''s Rational Interpolants[J]. Journal of Henan University of Science & Technology:Natural Science, 2006, 27(6): 83-86 |
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| Authors: | WANG Jia-Zheng |
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| Abstract: | Tri-variate rational function is structured by incorporating Thiele's branched continued fraction in bivariate Newton's interpolation polynomials.By defining tri-variate mixed difference and inverse difference,tri-variate rational interpolating algorithm is built,and interpolating characteristical theorem and its proof are given.A numerical example is presented to illustrate the efficiency of this algorithm.Tri-variate rational interpolating has direct application in geometrical modeling,image processing and CAGD,etc. |
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| Keywords: | Continued fraction Rational interpolation Inverse difference Characteristical theorem |
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