| Lagrange插指与Newton插指的注记 |
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| 引用本文： | 邹乐,李昌文.Lagrange插指与Newton插指的注记[J].合肥工业大学学报(自然科学版),2011(10). |
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| 作者姓名： | 邹乐 李昌文 |
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| 作者单位： | 合肥学院网络与智能信息处理重点实验室;淮北师范大学数学科学学院; |
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| 基金项目： | 安徽省教育厅重点科研资助项目(KJ2008A027); 安徽省高等学校省级自然科学研究资助项目(KJ2010B182;KJ2011B152); 合肥学院自然科学基金资助项目(11KY06ZR) |
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| 摘 要： | 文章对Lagrange插指多项式进行了改进,得到了改进的Lagrange插指多项式和重心型Lagrange插指多项式。重心型Lagrange插指多项式具有计算量小、数值计算稳定性好和增加新的插指节点不需重新计算原有插指节点基函数的优点。同时该文还讨论了Lagrange插指多项式与Newton插指多项式的相互转化,给出了与Newton插指多项式与Lagrange插指多项式相互转化的算法。
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| 关 键 词： | 插指多项式 Newton插指多项式 重心Lagrange插值 |
A note on interpolation polynomial in power exponent form:Lagrange versus Newton |
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| ZOU Le,LI Chang-wen.A note on interpolation polynomial in power exponent form:Lagrange versus Newton[J].Journal of Hefei University of Technology(Natural Science),2011(10). |
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| Authors: | ZOU Le LI Chang-wen |
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| Institution: | ZOU Le1,LI Chang-wen2(1.Key Laboratory of Network and Intelligent Information Processing,Hefei University,Hefei 230601,China,2.School of Mathematics,Huaibei Normal University,Huaibei 235000,China) |
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| Abstract: | In this paper,the Lagrange interpolation polynomial in power exponent form is improved and two new interpolation polynomials in power exponent form are derived,i.e.a modified Lagrange form and a barycentric Lagrange form.The advantages of the barycentric Lagrange form lie in its less computation and good numerical stability.Besides,when adding a new data pair,the barycentric form needs no recomputation of all the basis functions.The conversion algorithm of the Lagrange interpolation polynomial in power expo... |
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| Keywords: | interpolation polynomial in power exponent form Newton interpolation polynomial in power exponent form barycentric Lagrange interpolation |
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