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Observe, also, that the recurrence equation (6) can beretrieved from the recurrence equation (8).
Note that the preceding recurrence equation admits only one solution.
Clearly, the preceding Divide and Conquer recurrence equation can be retrieved as a particular case of the recurrence equation (5).
Hence (f_{S}) is a solution of the recurrence equation S.
Theorem 18 Let f T ∈ C c be the unique solution to the recurrence equation (5).
A recurrence equation of the form (6) has a unique solution f T ∈ RT c.
The harmonic responses of this kind of system are formulated by means of the recurrence equation method.
Next we want to emphasize that the Divide and Conquer recurrence equation (2) can betransformed into the recurrence equation S ( m ) = { c if m = 1, a S ( m − 1 ) + r ( m ) if m > 1, (15).
(7) It is clear that the fixed points of (Phi_{T}) are the solutions to the recurrence equation (5).
So, from engineering viewpoint, it remains to provide the asymptotic upper bound of the solution to the preceding recurrence equation.
Theorem 11 A recurrence equation of the form (8) has a unique solution f T ∈ RT c, k.
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