Question

用牛顿迭代法求方程X的3次方等于X加3的根,要求建立迭代格式,并且迭代2次,其中X零

其中X零等于0

Answer 1

x^3=x+3
x=(x+3)^(1/3)
f(x)=x-(x+3)^(1/3)
f'(x)=1-1/3*(x+3)^(-2/3)
X(n+1)=Xn-f(xn)/f'(xn)
x0=0
x1=1.7175
x2=1.6717
x3=1.6717
x4=1.6717
x5=1.6717

Answer 2

x^3=x+3
x=(x+3)^(1/3)
f(x)=x-(x+3)^(1/3)
f'(x)=1-1/3*(x+3)^(-2/3)
X(n+1)=Xn-f(xn)/f'(xn)
x0=0
x1=1.71747482978141
x2=1.67171989383679
x3=1.67169988166103
x4=1.67169988165716
x5=1.67169988165716