Newton's Method (Iteration 반복법, Newton-Raphson 뉴튼-랩슨법)

세상의 모든 계산기 수학, 과학, 공학 이야기 수학
Newton's Method (Iteration 반복법, Newton-Raphson 뉴튼-랩슨법)

- 세상의모든계산기
  *.78.140.87
- 2015.10.08 - 09:54 2015.03.23 - 11:21 1796 5

http://en.wikipedia.org/wiki/Newton's_method

$0 = f'(x_n) \, (x_{n+1}-x_n) + f(x_n).$

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}. \,\!$

이 게시물을..

세상의모든계산기 Lv. 25

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- 세상의모든계산기 (*.78.140.87) 2015.03.23 11:24 #comment_6043
  
  Square root of a number[edit]
  Consider the problem of finding the square root of a number. Newton's method is one of many methods of computing square roots.
  
  For example, if one wishes to find the square root of 612, this is equivalent to finding the solution to
  
  $\,x^2 = 612$
  The function to use in Newton's method is then,
  
  $\,f(x) = x^2 - 612$
  with derivative,
  
  $f'(x) = 2x. \,$
  With an initial guess of 10, the sequence given by Newton's method is
  
  $\begin{matrix} x_1 & = & x_0 - \dfrac{f(x_0)}{f'(x_0)} & = & 10 - \dfrac{10^2 - 612}{2 \cdot 10} & = & 35.6 \quad\quad\quad{} \\ x_2 & = & x_1 - \dfrac{f(x_1)}{f'(x_1)} & = & 35.6 - \dfrac{35.6^2 - 612}{2 \cdot 35.6} & = & \underline{2}6.395505617978\dots \\ x_3 & = & \vdots & = & \vdots & = & \underline{24.7}90635492455\dots \\ x_4 & = & \vdots & = & \vdots & = & \underline{24.7386}88294075\dots \\ x_5 & = & \vdots & = & \vdots & = & \underline{24.7386337537}67\dots \end{matrix}$
  where the correct digits are underlined. With only a few iterations one can obtain a solution accurate to many decimal places.
  
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- 세상의모든계산기 (*.165.6.43) 2015.10.08 09:54 #comment_7866
  
  fx-570 을 이용한 계산
  http://www.allcalc.org/7856
  
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- 세상의모든계산기 (*.78.140.87) 2015.03.23 11:53 #comment_6046
  
  http://kin.naver.com/qna/detail.nhn?d1id=11&dirId=1113&docId=221245100
  
  다음 연립방정식의 해를 구하라(단, 해들은 모두 소수점 이하 9째 자리까지 표기)
  
  y=x^2 과 y=e^(-x). 초기값=2
  
  처음에만 h(2) 이후에는 h(ans) ctrl + enter
  
  Attached file
  K-45.png 10.4KB / 102 K-46.png 13.0KB / 160
  
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- 세상의모든계산기 (*.78.140.87) 2015.03.23 12:59 #comment_6051
  
  ctrl+ENTER 로 구할 것
  
  Attached file
  K-47.png 6.0KB / 84
  
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- 세상의모든계산기 (*.78.140.87) 2015.03.24 10:54 #comment_6086
  
  9860G Recur 모드 이용
  
  Attached file
  K-76.png 44.7KB / 89 K-80.png 44.6KB / 127
  
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Newton's Method (Iteration 반복법, Newton-Raphson 뉴튼-랩슨법)

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Square root of a number[edit]