Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea...
Transcript of Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea...
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Newton-Raphson methodKorea University
Dept. of Chemical & Biological Engineering
9749007
![Page 2: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/2.jpg)
NR method의원리
f’(xi)
xi+2
f’(xi+1)
y=f(x)
xi+1 xi
f’(xi) = (xi - xi+1)f (xi)
f(xi)
0
xi+1 = xi -f’(xi)f (xi)
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Tayler Series에 의한 유도
xi+1 = xi -f’(xi)f (xi)
0 Approximation
![Page 4: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/4.jpg)
오차 분석
xi+1= true value xr
0
0
Et,i+1 Et,i
xrxr
Et,i+1 =-f’’(xr)2f’(xr)
Et,i2
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(dabs(delta).lt.error)
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문제점과 그 해결책1. 가능하면 프로그램 내에 그래프 기능 포함
2. 최종 근사값 함수에 대입해서 결과가 0에가까운지 검사
3. 프로그램의 최대 반복 횟수 제한
4. 프로그램은 계산 도중에 f’(x)=0이 되는가능성을 검사하여 사용자에게 알려줌
5.
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끝
9749007
![Page 8: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/8.jpg)
NR method의원리
f’(xi)
xi+2
f’(xi+1)
y=f(x)
xi+1 xi
f(xi)
0
![Page 9: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/9.jpg)
NR method의원리
f’(xi)
xi+2
f’(xi+1)
y=f(x)
xi+1 xi
f’(xi) = (xi - xi+1)f (xi)
f(xi)
0
xi+1 = xi -f’(xi)f (xi)
![Page 10: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/10.jpg)
Tayler Series에 의한 유도
0 Approximation
![Page 11: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/11.jpg)
Tayler Series에 의한 유도
xi+1 = xi -f’(xi)f (xi)
0 Approximation
![Page 12: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/12.jpg)
오차 분석
![Page 13: Newton-Raphson method Korea University - CHERIC · 2013-12-19 · Newton-Raphson method Korea University Dept. of Chemical & Biological Engineering 9749007](https://reader030.fdocuments.net/reader030/viewer/2022040209/5e48f6b09101e1686e74f718/html5/thumbnails/13.jpg)
오차 분석
xi+1= true value xr
0
Et,i+1 Et,i
xrxr
Et,i+1 =-f’’(xr)2f’(xr)
Et,i2