牛顿插值多项式python代码实现
时间: 2023-07-23 20:23:52 浏览: 105
以下是Python实现牛顿插值多项式的代码:
```python
import numpy as np
def newton_interpolation(x, y, x_new):
"""
使用牛顿插值多项式进行插值
:param x: 已知点的x坐标
:param y: 已知点的y坐标
:param x_new: 要插值的x坐标
:return: 对应的y值
"""
n = len(x)
# 初始化差商数组
f = np.zeros((n, n))
for i in range(n):
f[i, 0] = y[i]
for j in range(1, n):
for i in range(n - j):
f[i, j] = (f[i + 1, j - 1] - f[i, j - 1]) / (x[i + j] - x[i])
# 计算插值多项式
p = f[0, 0]
for i in range(1, n):
t = f[0, i]
for j in range(i):
t = t * (x_new - x[j])
p = p + t
return p
```
其中,x和y分别为已知点的x坐标和y坐标,x_new是要插值的x坐标。函数返回对应的y值。
相关问题
牛顿插值多项式python
以下是 Python 实现的牛顿插值多项式代码:
```python
def newton_interpolation(x, y):
"""
:param x: x 坐标序列
:param y: y 坐标序列
:return: 插值多项式
"""
n = len(x)
c = y.copy()
for k in range(1, n):
for i in range(n - 1, k - 1, -1):
c[i] = (c[i] - c[i - 1]) / (x[i] - x[i - k])
p = c[n - 1]
for i in range(n - 2, -1, -1):
p = c[i] + (x - x[i]) * p
return p
```
其中,`x` 和 `y` 分别为已知的 x 坐标序列和 y 坐标序列,函数返回插值多项式。
牛顿插值多项式实现python代码
牛顿插值法是一种通过已知数据点构建多项式函数来近似连续函数的数学技术。在Python中,我们可以使用numpy库来实现。以下是使用三个点(x0, y0), (x1, y1), 和 (x2, y2)创建二次(线性、二次)牛顿插值多项式的简单示例:
```python
import numpy as np
def newton_interpolation(points):
"""
Newton's Interpolation using numpy for a quadratic polynomial
:param points: List of tuples [(x0, y0), (x1, y1), (x2, y2)]
:return: Quadratic polynomial function
"""
x = [p[0] for p in points]
y = [p[1] for p in points]
# Calculate coefficients
A = np.array([[x[0]**2, x[0], 1],
[x[1]**2, x[1], 1],
[x[2]**2, x[2], 1]])
b = np.array([y[0], y[1], y[2]])
# Solve the system of equations to get the coefficients
coefficients = np.linalg.solve(A, b)
def interpolate(x_val):
return coefficients[0]*x_val**2 + coefficients[1]*x_val + coefficients[2]
return interpolate
# Example usage
points = [(0, 0), (1, 1), (2, 4)]
quad_poly = newton_interpolation(points)
print(quad_poly(1.5)) # Output: The approximate value at x=1.5
阅读全文