# How to generalize the fixed point iteration

1. Aug 14, 2012

### Charles49

If we want to solve $$f(x)=0$$ we can re-write the equation as
$$g(x)=x$$ and use the fixed point method, i.e, $$x_{n+1}=g(x_n)$$ starting with a guess $$x_0.$$ I was wondering if something similar can be done with
$$\Lambda(x,y)=h(x,y).$$

2. Aug 15, 2012

### HallsofIvy

Staff Emeritus
Yes, of course. Just think of (x, y) as a single two dimensional variable, z and solve g(z)= z.

3. Aug 15, 2012

### racefan4TX

Excellent info can be found about these kinds of boards. Thanks folks.

4. Aug 15, 2012

### Charles49

HallsofIvy,

What a simple solution!

Thanks