内积空间与最小二乘法

Inner Product Space and the Least Square Method

摘要: 最小二乘法在一般的线性代数中存在标准的推导过程。本文从内积空间的结构出发去发现最小二乘法的本质问题，并且给出了最小二乘法取值的快速算法。同时我们给出了在内积空间中多个点到子空间的最小距离的求法，这是对一般最小二乘的延托。The least square method has a standard method in most of books about linear algebra. In this paper we introduce the element definitions of inner product space and the standard least square method. And in this document we also give a fast calculation for the least square method in inner product space. In the least part we give a method for calculating the smallest distance of the sum of finite points to a subspace. This is an extension for the least square method.