Solving equations--fixed point iteration

Definition: If G (r) =r, then the real number r is a fixed point of function G.

If we have an equation f (x) = 0, which is indicated as a fixed point problem, there is: g (x) =x (Note: f (x) =g (x)-X)

The fixed point r is a root of the equation f (x) =0, which is the y=g (x) and the y=x of the intersection is the fixed point R

Algorithm Analysis: x0 = Initial Set value

x1 = g (x0)

x2 = g (x1)

x3 = g (x2)

...    ...

X (k+1) = g (x (k))

Until it converges to g (r) = g (Lim x (i)) = Lim X (i+1) = R

MATLAB Code implementation:

= FPI (g,x0,k)x(1) = x0;  for i = 1: k    x(i+1) = g (x (i));  End= x (k+1);

Solving equations--fixed point iteration