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x_{n+1} = x_n - f(x_n) / f'(x_n)

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  • x_n ÊÇµÚ n ´Îµü´úµÄ½üËÆÖµ
  • f(x_n) ÊÇ f(x) ÔÚ x_n ´¦µÄº¯ÊýÖµ
  • f'(x_n) ÊÇ f(x) ÔÚ x_n ´¦µÄµ¼ÊýÖµ

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ΪÁËÇó½â a £¬ÎÒÃÇÐèÒª½ç˵һ¸öº¯Êý g(x) = x^2 – a¡£ËüµÄ¸ù¾ÍÊÇÎÒÃÇËùÒªÕÒµÄ a¡£

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g'(x) = 2x

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x_{n+1} = x_n - (x_n^2 - a) / 2x_n

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x_{n+1} = (x_n^2 + a) / 2

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  • x_1 = (2^2 + 4) / 2 = 4
  • x_2 = (4^2 + 4) / 2 = 10
  • x_3 = (10^2 + 4) / 2 = 54

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