let g(x)=-11+10-6x²+2x³.
Assume that the equation g(x)=0 has a unique root α in [1,2]. with x <sub>0</sub> =1, find the number of iterations required to give the estimate of α correct to 4 d.p..
Numerical Analysis?
2017-04-17 5:49 pm
回答 (1)
2017-04-17 6:15 pm
By Newton's method
g(x)=-11+10x-6x^2+2x^3 (I think you miss a x)
g'(x)=10-12x+6x^2
x(n+1)=x(n)-g(x(n))/g'(x(n))
set x(1)=1
x(2)=1-g(1)/g'(1)=1-(-5)/4=2.25
x(3)=x(2)-3.90625/13.375=1.957944
x(4)=x(3)-0.589903/9.50594=1.895888
x(5)=x(4)-0.021659/8.815692=1.893431
x(6)=x(5)-3.11e-05/8.789314=1.893427
α~x(6)~1.8934
x(3)
g(x)=-11+10x-6x^2+2x^3 (I think you miss a x)
g'(x)=10-12x+6x^2
x(n+1)=x(n)-g(x(n))/g'(x(n))
set x(1)=1
x(2)=1-g(1)/g'(1)=1-(-5)/4=2.25
x(3)=x(2)-3.90625/13.375=1.957944
x(4)=x(3)-0.589903/9.50594=1.895888
x(5)=x(4)-0.021659/8.815692=1.893431
x(6)=x(5)-3.11e-05/8.789314=1.893427
α~x(6)~1.8934
x(3)
收錄日期: 2021-04-18 16:08:15
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170417094907AAZAQhg