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Let A be a given positive constant and g(x) = 2x Ax2. a. Show that if fixed-point

Chapter 2, Problem 16

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QUESTION:

Let A be a given positive constant and g(x) = 2x Ax2. a. Show that if fixed-point iteration converges to a nonzero limit, then the limit is p = 1/A, so the inverse of a number can be found using only multiplications and subtractions. b. Find an interval about 1/A for which fixed-point iteration converges, provided p0 is in that interval.

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QUESTION:

Let A be a given positive constant and g(x) = 2x Ax2. a. Show that if fixed-point iteration converges to a nonzero limit, then the limit is p = 1/A, so the inverse of a number can be found using only multiplications and subtractions. b. Find an interval about 1/A for which fixed-point iteration converges, provided p0 is in that interval.

ANSWER:

Step 1 of 4

(a)

If  is the fixed point for the function  then  for .

By fixed point theorem,

                                                               

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