# Iterative method

1. Jan 25, 2012

### bb.minhtri

1. The problem statement, all variables and given/known data

The iterative method is used to find the approximate root of the equation x3 + x - 1000 = 0 in [9, 10]. What is the suitable iterative function?

2. Relevant equations

3. The attempt at a solution
How to find the iterative function and is there any conditions for one?
Thanks for helps.

2. Jan 25, 2012

### ehild

The iterative procedure is to calculate the next approximation of x from a function of the previous approximation: xi+1=f(xi). The iterative process can converge in a range of x where the derivative |df/dx |<1.

You can try the ways: x=1000-x3 or x=(1000-x)^1/3.
Which one works? And you can find other iterative functions for this equation.

ehild

Last edited: Jan 25, 2012
3. Jan 25, 2012

### bb.minhtri

The second one works ^^ Thank you very much. Your explanation is very clear:D

4. Jan 25, 2012

### ehild

Using cubic root in an iteration process is not too nice. You can find an other method without that. Hint: write x^3-1000 in the form (x-10)(x^2+10x+100), and isolate x from the x-10 factor.

ehild