尊龙凯时人生就是搏

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Å£¶Ùµü´ú·¨ÊÇÒ»ÖÖµü´úÇó¸ùÒªÁ죬Õë¶Ô·½³Ì f(x) = 0£¬Æäµü´ú¹«Ê½Îª£ºx_{n+1} = x_n – f'(x_n) / f”(x_n)¡£¸ÃÒªÁìµÄʹÓð취°üÀ¨£ºÑ¡Ôñ³õʼֵ¡¢ÅÌËã x_{n+1}¡¢¼ì²éÊÕÁ²ÐÔ¡¢¸üеü´úÖµ£¬Öظ´Ç°Êö°ì·¨Ö±µ½ÊÕÁ²»òµÖ´ï×î´óµü´ú´ÎÊý¡£

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

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  • x? ÊdzõʼÍƲâÖµ
  • x? ÊÇµÚ n ´Îµü´úÖµ
  • f'(x) ÊÇ f(x) µÄÒ»½×µ¼Êý
  • f”(x) ÊÇ f(x) µÄ¶þ½×µ¼Êý

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  1. Ñ¡Ôñ³õʼֵ x?£ºÑ¡ÔñÒ»¸ö¿¿½ü·½³Ì¸ùµÄÖµ×÷Ϊ³õʼÍƲâ¡£
  2. ÅÌËã x?+1£ºÊ¹Óøø¶¨µÄ¹«Ê½ÅÌËã x?+1¡£
  3. ¼ì²éÊÕÁ²ÐÔ£ºÈôÊÇ |x?+1 – x?| СÓÚÉ趨µÄÎó²îÈÝÏÞ£¬Ôòµü´ú×èÖ¹¡£
  4. ¸üеü´úÖµ£º½« x?+1 ×÷ΪÏÂÒ»´Îµü´úµÄ x?¡£
  5. Öظ´°ì·¨ 2-4£ºÖ±µ½ÊÕÁ²»òµÖ´ï×î´óµü´ú´ÎÊý¡£

ʾÀý£º

Çó½â·½³Ì f(x) = x? – 2x? + x – 1 = 0¡£

  • ³õʼֵ£º x? = 1
  • Ò»½×µ¼Êý£º f'(x) = 3x? – 4x + 1
  • ¶þ½×µ¼Êý£º f”(x) = 6x – 4

µü´úÅÌË㣺

  • x? = 1 – (1? – 21? + 1 – 1) / (31? – 4*1 + 1) = 0.5
  • x? = 0.5 – (0.5? – 20.5? + 0.5 – 1) / (30.5? – 4*0.5 + 1) = 0.666667
  • x? = 0.666667 – (0.666667? – 20.666667? + 0.666667 – 1) / (30.666667? – 4*0.666667 + 1) ¡Ö 0.625

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