Question

Find an interval of unit length which contains the negative real root of .
Construct a fixed-point iteration , which converges. Verify the condition of convergence. Take the mid-point of this interval as a starting approximation and iterate thrice.
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Answer 1

Step-by-step explanation:

If the function f is continuously differentiable, a sufficient condition for convergence is that the spectral radius of the derivative is strictly bounded by one in a neighborhood of the fixed point. If this condition holds at the fixed point, then a sufficiently small neighborhood (basin of attraction) must exist.