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以线性代数观点看常用多项式插值方法
  • ISSN号：1008-1399
  • 期刊名称：《高等数学研究》
  • 时间：0
  • 分类：O241.3[理学—计算数学;理学—数学] O151.2[理学—数学;理学—基础数学]
  • 作者机构：华北理工大学理学院,河北唐山063009
  • 相关基金：中国自然科学基金项目（61170317,11601151）,河北省自然科学基金项目（A2013209295,A2015209189）,《数值计算方法》国家级精品资源共享课建设项目.
作者： 龚佃选, 刘春凤
关键词： 空间的基, LAGRANGE插值, Newton插值, TAYLOR公式, 过渡矩阵, vector basis, Lagrange Interpolation, Newton Interpolation, Taylor Formula, transition ma-trix
中文摘要：

数学各分支之间存在很多共同的思想和方法.本文结合线性代数中关于线性空间的相关理论及观点来看数值分析中常用的多项式插值方法.一方面借助线性空间的基与坐标理论将常用多项式插值方法统一起来,并借助过渡矩阵给出了不同插值方法之间的通用转换公式.另一方面还可以通过构造特殊基函数组来产生新的多项式插值方法.

英文摘要：

There are many common ideas and methods between the branches of mathematics. We reinter- pret the polynomial interpolations of numerical analysis via the related theory of linear space. Specifically, we unify different polynomial interpolations with the basis and coordinate theory of linear space, and give a general conversion formula between different int onstrate that new polynomial interpolations can erp be olation methods with transition matrices. We also demobtained by constructing special basis functions.

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期刊信息
  • 《高等数学研究》
  • 主管单位:陕西省科学技术协会
  • 主办单位:西北工业大学 陕西省数学会
  • 主编：
  • 地址：西安市友谊西路127号西北工业大学
  • 邮编：710072
  • 邮箱：gdsxyj@126.com
  • 电话：029-88491574
  • 国际标准刊号：ISSN：1008-1399
  • 国内统一刊号：ISSN：61-1315/O1
  • 邮发代号:52-192
  • 获奖情况:
  • 1997年获陕西省教学成果一等奖,2000年获陕西省优秀期刊一等奖
  • 国内外数据库收录:
  • 被引量:4507