Calculation method

  • Thread starter brad sue
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
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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.
 
  • #3
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iNCREDiBLE said:
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
 

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