Fixed Point Iteration: Why Change g(x) to Find Other Roots?

[brad sue]

Hi,
in the method -Theory of Fixed Point Iteration of x = g(x)

If the function g(x) has several roots, why sometimes we need to change the form of g(x) to find the other roots?

For example we can have x³+3x²+x+4,
one form can be x= -x³-3x²-4
or
another form can be
x=sqrt(-x³-3x²-4) / sqrt (3)

those two forms converge into diffrent values.WHY?

Thank you

Brad

 

[iNCREDiBLE]

You've misunderstood the whole thing!

Definition: A fixed point of a function g(x) is a number p such that p = g(p).

Caution. A fixed point is not a root of the equation 0 = g(x), it is a solution of the equation x = g(x).

Geometrically, the fixed points of a function g(x) are the point(s) of intersection of the curve y = g(x) and the line y = x.

 

[brad sue]

You've misunderstood the whole thing!

Definition: A fixed point of a function g(x) is a number p such that p = g(p).

Caution. A fixed point is not a root of the equation 0 = g(x), it is a solution of the equation x = g(x).

Geometrically, the fixed points of a function g(x) are the point(s) of intersection of the curve y = g(x) and the line y = x.

Ok that makes more sense now.

Thank you very much