Wikipedia:Reference desk/Archives/Mathematics/2018 April 29

= April 29 =

Solving a recurrence
What's the solution of $$T(n)=4T(n/3)+4T(2n/3)$$? עברית (talk) 18:29, 29 April 2018 (UTC)
 * One solution is $$T(n) = n^{3.612803505172812}$$ --catslash (talk) 00:34, 30 April 2018 (UTC)
 * More specifically, T(n) = kna is a solution where k is arbitrary and a is a root of the equation 3a=4(1+2a). Usually a recurrence is used to to define a function on integers, so this is more of a functional equation. --RDBury (talk) 00:51, 30 April 2018 (UTC)
 * More generally, since the equation is first degree homogeneous in T, it is satisfied by an arbitrary linear combination of $$n^{3.612803505172812}$$ and any other independent solution. --catslash (talk) 01:26, 30 April 2018 (UTC)
 * There are an infinite number of complex solutions for the exponent, but obviously the set of all these solutions won't form a complete set as an arbitrary $$T(n)$$ does not satisfy the recurrence. Count Iblis (talk) 06:36, 30 April 2018 (UTC)

Thank you very much! עברית (talk) 18:54, 1 May 2018 (UTC)