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A famous example is Strassen's matrix multiplication algorithm, whose running time satisfies the recurrence $T(n) = 7T(n/2) + O(n^2)$. A similar example is Karatsuba's algorithm for fast integer multiplication, whose running time satisfies the recurrence $T(n) = 3T(n/2) + O(n)$. Other algorithms for multiplying matrices or integers supply even more examples ...
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