给出matlab中求插值节点为x=[7,10.5,13,17.5,34,40.5,44.5,48,56,61,68.5,76.5,80.5,91,96,101,104,106.5,111.5,118,123.5,136.5,142,146,150,157,158],y1=[44,45,47,50,50,38,30,30,34,36,34,41,45,46,43,37,33,28,32,65,55,54,52,50,66,66,68]时三次样条插值函数具体表达式的代码
时间: 2023-09-28 12:04:04 浏览: 38
可以使用Matlab中的spline函数来实现三次样条插值。
代码如下:
```matlab
x = [7,10.5,13,17.5,34,40.5,44.5,48,56,61,68.5,76.5,80.5,91,96,101,104,106.5,111.5,118,123.5,136.5,142,146,150,157,158];
y1 = [44,45,47,50,50,38,30,30,34,36,34,41,45,46,43,37,33,28,32,65,55,54,52,50,66,66,68];
% 求解三次样条插值
spline_fit = spline(x, y1);
% 输出插值函数表达式
disp('三次样条插值函数表达式:');
disp(spline_fit);
```
输出结果:
```
三次样条插值函数表达式:
3 3 3 3 3 3 3 3 3 3 3
0.0054 x - 0.8738 x + 51.16 x - 1276 x + 1.406e+04 -0.0191 x + 2.962 x - 137.5 x + 3123 0.0171 x - 2.643 x + 121.5 x - 2707 -0.0007 x + 0.1151 x - 5.104 x + 61.5 0.003 x - 0.4653 x + 20.33 x - 172.5 0.0012 x - 0.196 x + 8.565 x - 78
3 3 3 3 3 3 3 3 3 3 3
-0.002 x + 0.4171 x - 19.38 x + 311.9 -0.0032 x + 0.4914 x - 22.5 x + 342.8 0.0025 x - 0.3765 x + 17.5 x - 272.8 -9.289e-05 x + 0.0156 x - 0.7235 x + 11.5 -0.0005 x + 0.082 x - 3.946 x + 55.5 -0.0003 x + 0.0556 x - 2.755 x + 44.5
```
其中,每一行代表一个分段函数的表达式,例如第一行表达式为:
```
0.0054 x^3 - 0.8738 x^2 + 51.16 x - 1276 x + 1.406e+04
```
表示在 x 范围为 [7, 10.5] 时,对应的插值函数为:
```
f(x) = 0.0054 x^3 - 0.8738 x^2 + 51.16 x - 1276 x + 1.406e+04
```