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曲线拟合在数学建模中的应用
目录
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
数学建模方法是处理科学理论的1种经典方法，也是解决各类实际问题的常用方法。通过抽象、简化、假设、引进变量等处理过程后，将实际问题用数学方式表达，建立起数学模型，然后运用先进的数学方法及计算机技术进行求解。曲线拟合通俗地讲就是用1条(或1族)适当的曲线去模拟1组(或多组)实验数据，从而得到较好地符合实验事实的数学关系式。MATLAB是1种广泛应用于工程计算及数值分析领域的新型高级语言。本文探讨了MATLAB这1强而有力的工具在实验数据分析和处理中的应用。将测量中得到的水塔流量的相关数据运用最小2乘法，通过编写程序实现向计算机输入实验测量数据，由MATLAB计算求出其函数表达式，明确表示出各物理量之间的关系。同时在屏幕上作出函数表达式的曲线，实现了数据分析和处理的快捷、准确和直观。计算结果与实际记录基本吻合。
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
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