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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(choose chapter or problem)
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.
Questions & Answers
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,