下列数据点的插值 x:0,1,4,9,16,25,36,49,64 y:0,1,2,3,4,5,6,7,8 (1)用python 求多项式插值L₈(x), (2) 用三次样条(第一边界条件)法求 S(x).
时间: 2024-03-18 14:35:53 浏览: 23
以下是使用Python进行多项式插值和三次样条插值的示例代码:
1. 多项式插值L₈(x):
```python
import numpy as np
from scipy.interpolate import lagrange
x = np.array([0, 1, 4, 9, 16, 25, 36, 49, 64])
y = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8])
poly = lagrange(x, y)
L8 = np.poly1d(poly)
# 求解插值结果
x_interpolated = np.linspace(0, 64, 100)
y_interpolated = L8(x_interpolated)
# 输出插值结果
print("多项式插值L₈(x)的结果:")
for i in range(len(x_interpolated)):
print("x = {:.2f}, y = {:.2f}".format(x_interpolated[i], y_interpolated[i]))
```
2. 三次样条插值S(x):
```python
from scipy.interpolate import CubicSpline
spline = CubicSpline(x, y, bc_type='natural')
# 求解插值结果
y_interpolated = spline(x_interpolated)
# 输出插值结果
print("三次样条插值S(x)的结果:")
for i in range(len(x_interpolated)):
print("x = {:.2f}, y = {:.2f}".format(x_interpolated[i], y_interpolated[i]))
```
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