27 lines
525 B
Python
27 lines
525 B
Python
def fx(x):
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return 1/x
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# 逐次分半梯形递推公式
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def SplitTrapezoidal(a,b,err):
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t1 = (b-a)*(fx(a)+fx(b))/2
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k = 1
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while True:
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tmp = 0
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for i in range(1, 2**(k-1)+1):
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tmp += fx(a + (b-a)*(2*i-1)/(2**k))
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t2 = t1/2+(b-a)*tmp/(2**k)
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if abs(t2-t1) < err:
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break
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t1 = t2
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k += 1
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return t2,k
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if __name__ == "__main__":
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a = 1
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b = 3
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err = 1e-2
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result,k = SplitTrapezoidal(a, b, err)
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print(f"Result: {result},k={k}")
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