曲线拟合在数学建模中的应用

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翻新时间：2023-08-05

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曲线拟合在数学建模中的应用

摘要 1

Abstract 2

前言 3

1 数学建模简介 4

1.1 数学建模的概念 4

1.2 数学建模的1般方法和步骤 4

1.3 数学建模的重要意义 4

2 MATLAB简介 5

2.1 组成 5

2.2 MATLAB语言 6

3 曲线拟合 8

3.1 曲线拟合理论 8

3.2 曲线拟合的最小2乘法 8

3.3 线性最小2乘法 9

3.4 直线拟合 10

3.5 多项式拟合 10

3.6 用MATLAB作线形最小2乘拟合 11

4 MATLAB与曲线拟合在水塔流量估计模型中的应用 14

4.1 问题的提出 14

4.2 问题分析 14

4.3 模型假设 14

4.4 流量估计的解题思路 15

4.5 算法设计与编程 15

4.6 分析与改进 23

5 结束语 24

参考文献 25

致谢 26

摘要

关键词：数学建模；曲线拟合；水塔流量

Abstract

Mathematics modelling is a classical method to the process scientific theory . Also, it’s a common method to solve all kinds of actual problems. Through the processing of abstract, simplification, supposition and introduction variable, we can express the actual problem with mathematics, establish the mathematical model, and adopt the advanced mathematics method and computer technology to carry on the solution . Generally speaking, the curve fitting is to use a suitable curve imitating, a group with (or multi-groups) the empirical datum, and then abtain mathematics relationship in line with the fact well. MATLAB is a new advanced language applying in the field of engineering calculation and the numerical analysis . This article will discuss MATLAB —— this powerful tool applying in the empirical datum analysis and processing. Utilize the relevant data about the flow of the water tower acquired in survey to realize the input of survey data for erperient into the computer ,first by way of the lowese square metheod and later through programming; then, the function expression will be worked out through MATLAB computation ,and the relationship between various physical volume can be showed clearly. Meanwhile the curve of function expression on the screen makes it quick, accurate and direct for figures analying and processing. The computed result corresponds to the real record basically.

Key words：mathematics modeling; curve fitting ; water tank current capacity