Fixed Point Iteration for Solving Equations

[Huumah]

Homework Statement

Apply fixed point iteration to find the solution of each equation to eight correct decimal places

x³=2x+2

The Attempt at a Solution

I have tried to rewrite the equation for in every possible way to solve for one x and pluggin in my guess( have tried -2,-1,0,1,2,3,4)

and finding x₁ and then x₂ and plugging them all inn seperatly.

But my answer switches from positive values to negative values and never seems to be converging to the answer which is 1.76929235


I can understand the sample problem but I'm stuck on this problem.

 

[Mark44]

Homework Statement

Apply fixed point iteration to find the solution of each equation to eight correct decimal places

x³=2x+2

The Attempt at a Solution

I have tried to rewrite the equation for in every possible way to solve for one x and pluggin in my guess( have tried -2,-1,0,1,2,3,4)

and finding x₁ and then x₂ and plugging them all inn seperatly.

The formula you show above is incorrect. It should be
$$ x_{n+1} = \frac{2(x_n + 1)}{x_n^2}$$

But my answer switches from positive values to negative values and never seems to be converging to the answer which is 1.76929235I can understand the sample problem but I'm stuck on this problem.

If you start with x₀ = 1, what are the next three numbers you get?
If you start with x₀ = 2, what are the next three numbers you get?

 

[jfgobin]

Don't forget that there are conditions for a function to have a fixed point.

The expression I used is:

$x_{n+1}=\sqrt { \frac { 2\left ( x_n + 1 \right )}{x_n} }$
​

Try with $x_0 = 1$ and $x_0 = 2$ and let me know.

J.