Basic project in Continuous system simulation

###Program 1 - Data Interpolation

• Lagrange Interpolation;
• Newton Interpolation;
• If you want to use your own data, please ensure the data layout in input.txt and testx.txt is same to the original file;
• Ensure all the file below are in the same path;
• Detailed annotations are in the file.

File Name	Application
main.cpp	main program to run
input.txt	Given Data
testx.txt	Data X to calculate
Result.txt	Result saved in this file(show after running)

###程序1 - Data Interpolation

• 拉格朗日插值法；
• 牛顿插值法；
• 如果你想使用你自己的数据，请确保数据输入及存储的格式同原始的input.txt和testx.txt是一致的；
• 请确保以下的文件均放在同一个文件夹之下；
• 更细节的注释在文档中。

文件名	含义
main.cpp	待运行的主程序
input.txt	已知的数据对
testx.txt	待求的数据
Result.txt	存储结果的文件（主程序运行之后才会出现）

Program 2 - Data Fitting

• Using least square method to do data fitting, includings the solution of linear equation by Newton Elimination Method and LU Decomposition Method.

1. Solution of linear equation

Transfer the equations into augmented matrix. 1.1 Gaussian Elimination Method The whole process divided into 2 parts, elimination and inverse calculayion. Actually, it transfer the augmented matrix into upper triangular matrix and then, do iteration from the bottom to the upper. 1.2 LU Decomposition Method On the basis of gaussian elimination, its idea is to divide the augmented matrix into 2 triangular matrixes. The detaled LU Decomposition formula please check other sources.

2. Least Sqaure Method

The fitted degree of a polynomal can be and must be assigned by the user in the window when the program is running. For example, When $degree=2$, $$y = a_0+a_1x+a_2x^2$$ When $degree=3$, $$y = a_0+a_1x+a_2x^2+a_3x^3$$ When $degree=4$, $$y = a_0+a_1x+a_2x^2+a_3x^3+a_4x^4$$ Be attention that the assigned term cannot be bigger than the amount ot data you give.

• The detailed results are saved in the file, named computation_sheet.txt,including the degree of fitting polynomial you assigned, exact fitted polymonial and calculated data.
• If you want to use your own data, please ensure the data layout in rawData.txt and x2Calculate.txt is same to the original file. For example, line 1 in rawData.txt is data x, and line 2 is data y, while there is only one line in x2Calculate.txt.

File Name	Application
fitting.cpp	main program to run
rawData.txt	Given Data
x2Calculate.txt	Data X to calculate
computation_sheet.txt	Result saved in this file(show after running)

PS. The develop environment is Windows 7 + Visual Studio 2017