牛頓拉弗森法解方程式
回答 (3)
2012-10-31 9:02 pm
✔ 最佳答案
令f(x)=x^3-20df(x)/dx=3x^2
△c(0)=c-f(x(0))=0-l 3^3-20 l=-7
[df/dx]=3*3^2=27
△x(0)=c(0)/[df/dx](0)=-7/27=-0.259
x(1)=x(0)+△x(0)=3-0.259=2.741
x(2)=x(1)+△x(1)=2.741-(0.593/22.539)=2.715
x(3)=x(2)+△x(2)=2.715-)0.012/22.113)=2.7144
x值約為2.7144
2012-11-01 7:45 pm
他數學可能比老師強!
2012-10-31 10:32 pm
牛頓拉弗森法
x_n+1 = x_n - f(x_n)/f'(x_n)
f(x) = x^3 - 20, f'(x) = 3x^2
x_n+1 = x_n - [(x_n)^3 - 20]/[3x_n^2]
x_0 = 3
x_1 =3 - 7/27 = 2.740741
x_2 = 2.740741 - [(2.740741)^3 - 20]/[3 * 2.740741^2] = 2.714669625
x_3 = 2.71441764
x_4 = x_5 = x_6 = ... = 2.714417617
因此x^3 = 20 的根為2.714417617
x_n+1 = x_n - f(x_n)/f'(x_n)
f(x) = x^3 - 20, f'(x) = 3x^2
x_n+1 = x_n - [(x_n)^3 - 20]/[3x_n^2]
x_0 = 3
x_1 =3 - 7/27 = 2.740741
x_2 = 2.740741 - [(2.740741)^3 - 20]/[3 * 2.740741^2] = 2.714669625
x_3 = 2.71441764
x_4 = x_5 = x_6 = ... = 2.714417617
因此x^3 = 20 的根為2.714417617
收錄日期: 2021-04-27 17:44:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20121031000015KK02431