Problem

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

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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Solutions For Problems in Chapter 2.2