Fixed Point Iteration
Fixed Point Iteration is a successive substitution.
Rearranging f(x) = 0 so that x is on the left hand side of the equation.
X = g(x)
A fixed point for a function is a number at which the value of the function does not change when the function is applied.
g(x) = x
x = fixed point
Transformation can be accomplished either by algebraic manipulation or by simply adding x to both sides of the original equations.
Example:
Given a function of : X^4 + 2X^2 – X – 3
a.) g(x) = (3 + X -2X^2)^(1/4)
b.) g(x) = ((X + 3 – X^4)/2)^(1/4)
Rearranging f(x) = 0 so that x is on the left hand side of the equation.
X = g(x)
A fixed point for a function is a number at which the value of the function does not change when the function is applied.
g(x) = x
x = fixed point
Transformation can be accomplished either by algebraic manipulation or by simply adding x to both sides of the original equations.
Example:
Given a function of : X^4 + 2X^2 – X – 3
a.) g(x) = (3 + X -2X^2)^(1/4)
b.) g(x) = ((X + 3 – X^4)/2)^(1/4)