lhye200/CalWay_Python
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lwj
2025-06-13 20:43:17 +08:00
parent a7bd2092a4
commit 01e3e1732b
1 changed files with 12 additions and 9 deletions
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69-3.py
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@@ -1,8 +1,5 @@
import math import math
list_x = [0.0,0.2,0.4,0.6,0.8]
list_y = [1.0,1.2214,1.4918,1.8221,2.2255]
# 定义原函数和其导函数计算结果 # 定义原函数和其导函数计算结果
def FxDiff_n(x,n): def FxDiff_n(x,n):
return math.exp(x) return math.exp(x)
@@ -22,15 +19,16 @@ def GetDyList(list_y):
def NewtonForwardRegression(x,n,list_x): def NewtonForwardRegression(x,n,list_x):
h = list_x[1] - list_x[0] h = list_x[1] - list_x[0]
t = (x - list_x[0]) / h t = (x - list_x[0]) / h
ks = max([abs(FxDiff_n(list_x[i],n+1)) for i in range(n+1)]) ks = max([abs(FxDiff_n(list_x[i],n)) for i in range(n)])
result = 1 result = 1
for i in range(n+1): for i in range(n):
result *= (t-i)*h/(i+1) result *= (t-i)*h/(i+1)
return result * ks return result * ks
# 牛顿前插 # 牛顿前插
def NewtonForwardInterpolation(x,n,list_x,list_y): def NewtonForwardInterpolation(x,n,list_x,list_y):
list_dyk = GetDyList(list_y) list_dyk = GetDyList(list_y)
print(list_dyk)
h = list_x[1] - list_x[0] h = list_x[1] - list_x[0]
t = (x - list_x[0]) / h t = (x - list_x[0]) / h
result = list_y[0] result = list_y[0]
@@ -57,6 +55,7 @@ def GetDQyList(list_x,list_y):
# 牛顿基本插值 # 牛顿基本插值
def NewtonBaseInterpolation(x,n,list_x,list_y): def NewtonBaseInterpolation(x,n,list_x,list_y):
list_dqy = GetDQyList(list_x,list_y) list_dqy = GetDQyList(list_x,list_y)
print(list_dqy)
result = list_dqy[0][0] result = list_dqy[0][0]
mul = 1 mul = 1
for i in range(1,n): for i in range(1,n):
@@ -65,7 +64,11 @@ def NewtonBaseInterpolation(x,n,list_x,list_y):
return result return result
if __name__ == '__main__': if __name__ == '__main__':
print("三点牛顿前插 e^0.12 结果为%f, 截断误差%f" % NewtonForwardInterpolation(0.12, 2, list_x, list_y))
print("四点牛顿前插 e^0.12 结果为%f, 截断误差%f" % NewtonForwardInterpolation(0.12, 3, list_x, list_y)) list_x = [0.0,0.2,0.4,0.6,0.8] #改成题干的数值##############################3
print("三点牛顿基本插值 e^0.12 结果为%f" % NewtonBaseInterpolation(0.12, 2, list_x, list_y)) list_y = [1.0,1.2214,1.4918,1.8221,2.2255] #改成题干的数值##############################3
print("四点牛顿基本插值 e^0.12 结果为%f" % NewtonBaseInterpolation(0.12, 3, list_x, list_y)) print("三点牛顿前插 e^0.12 结果为%f, 截断误差%f" % NewtonForwardInterpolation(0.12, 3, list_x, list_y))
print("四点牛顿前插 e^0.12 结果为%f, 截断误差%f" % NewtonForwardInterpolation(0.12, 4, list_x, list_y))
print("三点牛顿基本插值 e^0.12 结果为%f" % NewtonBaseInterpolation(0.12, 3, list_x, list_y))
print("四点牛顿基本插值 e^0.12 结果为%f" % NewtonBaseInterpolation(0.12, 4, list_x, list_y))
#70到73行，0.12改成题干的数值，n是点数################################