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曲线拟合的最小一乘法

顾乐民

同济大学学报(自然科学版)2011,Vol.39Issue(9):1377-1382,6.
同济大学学报(自然科学版)2011,Vol.39Issue(9):1377-1382,6.DOI:10.3969/j.issn.0253-374x.2011.09.023

曲线拟合的最小一乘法

Least Absolute Deviation Method of Curve Fitting

顾乐民1

作者信息

  • 1. 同济大学材料科学与工程学院,上海201804
  • 折叠

摘要

Abstract

The solution of least absolute deviation (LAD),a pending problem for more than 200 years in mathematics, is not easy to calculate because of the absolute value function. Based on a great deal of computing and long-term study of various mathematical models under LAD criteria, a conclusion is drawn that if there is a LAD parameter a = a* ∈Rn, andmaking the following LAD criterion tenable mΣi=I/gi-f(χi,a* ) | = min, then the fitting function fI(χ, a* ) can be characterized that there are at least n points χ1,χ2,???,xn, making gi - f(χi,a*) =0,I = 1,2, ??? ,n(n≤m) valid,the problem of LAD solution can be achieved.

关键词

曲线拟合/最小一乘/逼近

Key words

urve fitting/least absolute deviation/approximation

分类

数理科学

引用本文复制引用

顾乐民..曲线拟合的最小一乘法[J].同济大学学报(自然科学版),2011,39(9):1377-1382,6.

同济大学学报(自然科学版)

OA北大核心CSCDCSTPCD

0253-374X

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