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曲線擬合在數學建模中的應用
目錄
摘 要 1
Abstract 2
前言 3
1 數學建模簡介 4
1.1 數學建模的概念 4
1.2 數學建模的1般方法和步驟 4
1.3 數學建模的重要意義 4
2 MATLAB簡介 5
2.1 組成 5
2.2 MATLAB語言 6
3 曲線擬合 8
3.1 曲線擬合理論 8
3.2 曲線擬合的最小2乘法 8
3.3 線性最小2乘法 9
3.4 直線擬合 10
3.5 多項式擬合 10
3.6 用MATLAB作線形最小2乘擬合 11
4 MATLAB與曲線擬合在水塔流量估計模型中的應用 14
4.1 問題的提出 14
4.2 問題分析 14
4.3 模型假設 14
4.4 流量估計的解題思路 15
4.5 算法設計與編程 15
4.6 分析與改進 23
5 結束語 24
參考文獻 25
致謝 26
摘 要
數學建模方法是處理科學理論的1種經典方法，也是解決各類實際問題的常用方法。通過抽象、簡化、假設、引進變量等處理過程后，將實際問題用數學方式表達，建立起數學模型，然后運用先進的數學方法及計算機技術進行求解。曲線擬合通俗地講就是用1條(或1族)適當的曲線去模擬1組(或多組)實驗數據，從而得到較好地符合實驗事實的數學關系式。MATLAB是1種廣泛應用于工程計算及數值分析領域的新型高級語言。本文探討了MATLAB這1強而有力的工具在實驗數據分析和處理中的應用。將測量中得到的水塔流量的相關數據運用最小2乘法，通過編寫程序實現向計算機輸入實驗測量數據，由MATLAB計算求出其函數表達式，明確表示出各物理量之間的關系。同時在屏幕上作出函數表達式的曲線，實現了數據分析和處理的快捷、準確和直觀。計算結果與實際記錄基本吻合。
關鍵詞：數學建模；曲線擬合；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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