51 lines
1.5 KiB
Python
51 lines
1.5 KiB
Python
import math
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# 牛顿方法求解方程
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def NewtonSolve(fx, dfx, x0, err, N0):
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count = 0
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print(f"k={count}, x0={x0}")
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x1 = x0 + 1 + err
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while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
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if abs(dfx(x1)) < 1e-10:
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return None, 0
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x1 = x0 - fx(x0) / dfx(x0)
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count += 1
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print(f"k={count}, x{count}={x1},x1-x0={abs(x1-x0)}")
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if count > N0:
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return None, -1
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x0 = x1
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return x1, 1
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# 查找根区间
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def FindRootZone(fx,start,stop,step):
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x = start
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while x < stop:
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if fx(x) * fx(x+step) < 0:
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return x
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x += step
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return None
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# 定义原函数 ###############################
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def fx(x):
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return x**2 + 10*math.cos(x)
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# 定义其导函数 ###############################
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def dfx(x):
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return 2*x - 10*math.sin(x)
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if __name__ == "__main__":
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##############################################################################################################
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err = 1e-5 # 根的误差限 见P141
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N0 = 100 # 最大迭代次数
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x0 = 1.6 # 可以指定初始值
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# x0 = FindRootZone(fx, 0, 2, 0.1) # 也可以用找根函数给定范围找根的缩小范围
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result,status = NewtonSolve(fx, dfx, x0, err,N0)
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if status == 1:
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print(f"fx收敛 解为: {result}")
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elif status == -1:
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print("fx不收敛")
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else:
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print("fx导数为0，无法收敛")
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