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$$x_{n+1} = x_n – \frac{f(x_n)}{f'(x_n)}$$

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  • (x_n) ÊÇÄ¿½ñµÄ½üËÆÖµ
  • (f(x)) ÊÇÄ¿µÄ·½³Ì
  • (f'(x)) ÊÇÄ¿µÄ·½³ÌµÄµ¼Êý

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  1. Ñ¡Ôñ³õʼֵ£ºÑ¡ÔñÒ»¸öÀë·½³Ì¸ù½Ï½üµÄ³õʼֵ (x_0)¡£
  2. µü´ú£ºÊ¹Óõü´ú¹«Ê½ (x_{n+1} = x_n – \frac{f(x_n)}{f'(x_n)}) Öظ´ÅÌËã £¬Ö±µ½Öª×ã×èÖ¹×¼Ôò¡£
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    • (x_1 = x_0 – \frac{x_0^2 – 5}{2x_0} = 2.5)
    • (x_2 = x_1 – \frac{x_1^2 – 5}{2x_1} \approx 2.24)
    • (x_3 = x_2 – \frac{x_2^2 – 5}{2x_2} \approx 2.236)
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  • ½üËƽ⣺(x \approx 2.236)

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