插值与拟合、趋势函数、VC++
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插值与拟合 Interpolation and Fitting
起草：杨鹏辉
2017.02.27~03.15
第
1
页 共
34
页
Interpolation and Fitting 插值与拟合-V2.1
1. 前言 Preface
................................................................................................................................................................................2
2. 插值与拟合 Interpolation and Fitting
..................................................................................................................................2
2.1. 最小二乘法理论基础（The basic theory of Least Squares Method）
.............................................................. 3
2.2. 数据拟合和曲线拟合（Data Fitting & Curve Fitting）
.......................................................................................... 3
3. 不同曲线的拟合模型
...................................................................................................................................................................4
3.1. 线性模型 Y=C
1
+C
2
X...................................................................................................................................................... 4
3.2. 拋物线模型 y=C
1
+C
2
X+C
3
X
2
2
1 2 3
y C C x C x
.........................................................................................5
3.3. 对数模型 Y=C
1
+C
2
ln(x)...............................................................................................................................................5
3.4. 指数模型 y=ae
bx
............................................................................................................................................................. 5
3.5. 双曲模型 y=1/(C1+C2X)............................................................................................................................................ 6
3.6. 幂模型 Power y=x
n
........................................................................................................................................................6
3.7. 多项式拟合 Polynomial Fitting...................................................................................................................................6
3.7.1. 多项式拟合原理（共 6 步）
................................................................................................................................6
3.7.2. 多元函数求偏导的推导过程（共 7 步）
......................................................................................................... 10
3.7.3. 线性方程组解法－LU 分解法（共 4 步）
....................................................................................................... 15
3.7.4. 矩阵 A 的 LU 分解的流程图（共 8 步）
..........................................................................................................18
4. 最小二乘法拟合范例 Example of Fitting by Least Squares Method..........................................................................29
4.1. 先验证算法正确性..........................................................................................................................................................29
4.2. 利用最小二乘法计算最优曲线..................................................................................................................................... 29
4.3. VS2010 中动态内存的申请...........................................................................................................................................30
5. 添加绘画控件............................................................................................................................................................................. 31
6. 参考资料及课本错误之处.........................................................................................................................................................33
6.1. 参考资料..........................................................................................................................................................................33
6.2. 课本上的错误之处..........................................................................................................................................................33
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