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March 8th, 2015, 05:05 PM   #1
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Solving a recurrence asymptotically

How can one solve the following recurrence asymptotically - that is, how can one find an explicit function $f(n)$ such that $T(n) = \Theta(f(n))$?

$T(n) =
\begin{cases}
\Theta(1) & \text{if $n\le 7, $} \\[2ex]
4T(\lceil{n/2}\rceil) + \Theta(n^2logn) & \text{if $n \gt 7.$}
\end{cases}$
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