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´ºÆ°-·¦½¼¹ý(Newton-Raphson Method)

ÀÛ¼ºÀÚ Uploader : nemesis ÀÛ¼ºÀÏ Upload Date: 2008-11-18º¯°æÀÏ Update Date: 2008-11-18Á¶È¸¼ö View : 7346

´ºÆ°-·¦½¼¹ý(Newton-Raphson Method)

¹ÌºÐ°¡´ÉÇÑ ÇÔ¼ö(f(x))ÀÇ Çظ¦ ±¸ÇÏ´Â ¼öÄ¡Çؼ®¹æ¹ýÀ¸·Î ÀÓÀÇÀÇ x1¿¡¼­ f(x)¿¡ Á¢ÇÏ´Â Á¢¼±ÀÇ ¹æÁ¤½ÄÀ» ±¸ÇÏ°í Á¢¼±°ú xÃà°úÀÇ ±³Á¡À» ±¸ÇÑ ÈÄ ±³Á¡¿¡¼­ÀÇ x2¸¦ ÀÌ¿ëÇÏ¿© ´Ù½Ã f(x2)¿¡ Á¢ÇÏ´Â Á¢¼±°ú Á¢¼±ÀÌ xÃà°ú ¸¸³ª´Â ±³Á¡À» ±¸Çϸç, À̸¦ ¹Ýº¹ÇÔÀ¸·Î½á f(x)ÀÇ Çظ¦ ±¸ÇÏ´Â ¹æ¹ýÀÌ´Ù. (±×¸² ÂüÁ¶)

f(x) : ¹ÌºÐ°¡´ÉÇÑ ÇÔ¼ö
f'(x) : f(x)ÀÇ ¹ÌºÐÇÔ¼ö
y : Á¢¼±ÀÇ ¹æÁ¤½Ä

y = f'(x1)x+b À̹ǷΠy1 = f'(x1)x1+b ÀÌ°í
b = y1 - f'(x1)x1 ÀÌ µÈ´Ù.
µû¶ó¼­, Á¢¼±ÀÇ ¹æÁ¤½Ä y´Â  
y = f'(x1)x + y1 - f'(x1)x1 ÀÌ´Ù.
x Ãà°úÀÇ ±³Á¡Àº y = 0 À̹ǷÎ
f'(x1)x2 = f'(x1)x1 - y1
x2 = x1 - y1/f'(x)
y1 = f(x1) À̹ǷÎ
x2 = x1 - f(x1)/f'(x1) ÀÌ µÈ´Ù.  

¼ö½Ä¿¡¼­ f(x1)Àº fx1À¸·Î
f(x1)ÀÇ ¹ÌºÐ°ªÀº gx1À¸·Î Ç¥±âÇß½À´Ï´Ù.

*** Âü°í¹®Çå[References] ***

x2 = x1 - fx1 / gx1
ÀÛ¼ºÀÚÀÇ ¼ö½Ä±×¸²ÀÌ ¾ø½À´Ï´Ù. No picture for this formula
º¯¼ö¸í Variable º¯¼ö°ª Value º¯ ¼ö ¼³ ¸í Description of the variable


¡Ø ÀÌ »çÀÌÆ®´Â ±¤°í¼öÀÍÀ¸·Î ¿î¿µµË´Ï´Ù.

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  • Ãʱ⠺¯¼ö°ªÀº f(x) = x^2 - 3x + 2 ÀÌ°í, ÃʱⰪÀ» 4 ·Î Àâ¾ÒÀ»¶§, f(4) = 6, f'(4) = 5 °¡ µÇ¹Ç·Î x2 = 2.8 ÀÌ µÇ´Â ¿¹ ÀÔ´Ï´Ù.
    ¸î¹ø ´õ °è»ê Çϸé, ÇØ 1, 2 Áß¿¡¼­ 2¿¡ Á¢±ÙÇÏ°ÚÁÒ..

    nemesis
    [2007-06-10 17:18:57]
  • Newton-Raphson ÀÌ ¸Â´Â öÀÚÁÒ

    m3d29
    [2007-06-22 20:36:31]
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    nemesis
    [2008-11-18 22:59:28]
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