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。
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 com- putation 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 interpola- tion polynomial in power exponent form into the Newton interpolation polynomial in power exponent form, and the conversion algorithm of the Newton interpolation polynomial in power exponent form into the Lagrange interpolation polynomial in power exponent form are both discussed.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第10期1580-1583,共4页
Journal of Hefei University of Technology：Natural Science
基金
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)
关键词
插指多项式
Newton插指多项式
重心Lagrange插值
interpolation polynomial in power exponent form
Newton interpolation polynomial in power exponent form
barycentric Lagrange interpolation
