. Suppose that the sequence (xn) satisfies |xn –α| ≤ c | xn-1- α|2 for all...

. Suppose that the sequence (x_n) satisfies

|x_n –α| ≤ c | x_n-1- α|² for all n.

Show by induction that c | x_n- α| ≤ c | x₀ - α|²ⁿ , and give some condition

That is sufficient for the convergence of (x_n) to α.

Use part a) to estimate the number of iterations needed to reach accuracy

|x_n –α| < 10^-12 in case c = 10 and |x₀ –α |= 0.09.

Expert Solution

Colby Messinger answered 3 years ago

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