基于空间投影的函数最佳平方逼近注记  

A Note on Best Approximation of Functions via Space Projection

作　　者：倪倩 王旭辉[3] Ni Qian;WANG Xuhui(School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematics,Hohai University,Nanjing 211100,China)

机构地区：[1]南京工业大学数理科学学院,南京211816 [2]中国科学院数学与系统科学研究院,北京100190 [3]河海大学数学学院,南京211100

出　　处：《大学数学》2023年第6期67-70,共4页College Mathematics

基　　金：中央高校基本科研业务费专项资金资助(423138);江苏省高等学校自然科学研究项目(22KJB110015)。

摘　　要：将线性代数中的向量空间投影理论应用到函数最佳逼近,最小二乘法与微分方程Galerkin方法求解问题中,一方面,将不同学科之间交叉融合,开阔学生视野培养学生融会贯通的能力;另外一方面,从几何的角度处理,直观、学生容易理解;从而为从事相关课程教学的老师提供一定的参考.Using the theory of projection of vectors in linear algebra,the teaching of the best approximation of functions,least square approximation,Galerkin method are unified,which facilitate the students to integrate the knowledge from different topics,broaden their sight and achieve mastery through a comprehensive study of the subject.Dealing the best approximation from the viewpoint of the geometry will make this topic easy to understand,which will also provide a certain reference for teachers engaged in the teaching of related courses.

关 键 词：空间投影 函数最佳逼近 最小二乘法 GALERKIN方法 

分 类 号：O151.2[理学—数学]