74 lines
2.4 KiB
Python
74 lines
2.4 KiB
Python
import math
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# 定义原函数和其导函数计算结果
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def FxDiff_n(x,n):
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return math.exp(x)
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# 求差分表
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def GetDyList(list_y):
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result = []
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result.append(list_y)
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for i in range(len(list_y)-1,0,-1):
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tmp = []
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for j in range(i):
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tmp.append(result[len(list_y)-1-i][j+1] - result[len(list_y)-1-i][j])
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result.append(tmp)
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return result
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# 牛顿前插余项计算
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def NewtonForwardRegression(x,n,list_x):
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h = list_x[1] - list_x[0]
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t = (x - list_x[0]) / h
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ks = max([abs(FxDiff_n(list_x[i],n)) for i in range(n)])
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result = 1
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for i in range(n):
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result *= (t-i)*h/(i+1)
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return result * ks
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# 牛顿前插
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def NewtonForwardInterpolation(x,n,list_x,list_y):
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list_dyk = GetDyList(list_y)
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print(list_dyk)
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h = list_x[1] - list_x[0]
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t = (x - list_x[0]) / h
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result = list_y[0]
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mul = 1
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result = list_y[0]
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for i in range(1, n):
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mul *= ((t-i+1)/i)
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result += list_dyk[i][0] * mul
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r = abs(NewtonForwardRegression(x,n,list_x))
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return (result,r)
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# 求差商表
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def GetDQyList(list_x,list_y):
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result = []
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result.append(list_y)
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for i in range(len(list_y)-1,0,-1):
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tmp = []
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for j in range(i):
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tmp.append((result[len(list_y)-1-i][j+1] - result[len(list_y)-1-i][j])/(list_x[j+len(list_y)-i] - list_x[j]))
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result.append(tmp)
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return result
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# 牛顿基本插值
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def NewtonBaseInterpolation(x,n,list_x,list_y):
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list_dqy = GetDQyList(list_x,list_y)
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print(list_dqy)
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result = list_dqy[0][0]
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mul = 1
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for i in range(1,n):
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mul *= (x - list_x[i-1])
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result += list_dqy[i][0] * mul
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return result
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if __name__ == '__main__':
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list_x = [0.0,0.2,0.4,0.6,0.8] #改成题干的数值##############################3
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list_y = [1.0,1.2214,1.4918,1.8221,2.2255] #改成题干的数值##############################3
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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))
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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))
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print("三点牛顿基本插值 e^0.12 结果为%f" % NewtonBaseInterpolation(0.12, 3, list_x, list_y))
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print("四点牛顿基本插值 e^0.12 结果为%f" % NewtonBaseInterpolation(0.12, 4, list_x, list_y))
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#70到73行，0.12改成题干的数值，n是点数################################ |