Asymptotics of Divide-And-Conquer Recurrences Via Iterated Function Systems
نویسنده
چکیده
fn = (k −mod(n, k))fbn/kc +mod(n, k)fdn/ke + an, n ≥ k, there is a unique continuous periodic function f∗ : R→ R with period 1 such that fn = nf(logk n)+o(n). If (an) is periodic with period k, ak = 0, and the initial conditions (fi : 1 ≤ i ≤ k − 1) are all zero, we obtain a specific iterated function system S, consisting of k continuous functions from [0, 1] × R into itself, such that the attractor of S is {(x, f∗(x)) : 0 ≤ x ≤ 1}. Using the system S, an accurate plot of f∗ can be rapidly obtained.
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