Search results
Results from the WOW.Com Content Network
Sections 4.3 (The master method) and 4.4 (Proof of the master theorem), pp. 73–90. Michael T. Goodrich and Roberto Tamassia. Algorithm Design: Foundation, Analysis, and Internet Examples. Wiley, 2002. ISBN 0-471-38365-1. The master theorem (including the version of Case 2 included here, which is stronger than the one from CLRS) is on pp. 268 ...
In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes.
Mason–Stothers theorem (polynomials) Master theorem (analysis of algorithms) (recurrence relations, asymptotic analysis) Maschke's theorem (group representations) Matiyasevich's theorem (mathematical logic) Max flow min cut theorem (graph theory) Max Noether's theorem (algebraic geometry) Maximal ergodic theorem (ergodic theory)
In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include: Master theorem (analysis of algorithms), analyzing the asymptotic behavior of divide-and-conquer algorithms; Ramanujan's master theorem, providing an analytic expression for the Mellin ...
The closed form follows from the master theorem for divide-and-conquer recurrences. The number of comparisons made by merge sort in the worst case is given by the sorting numbers . These numbers are equal to or slightly smaller than ( n ⌈ lg n ⌉ − 2 ⌈lg n ⌉ + 1), which is between ( n lg n − n + 1) and ( n lg n + n + O(lg n )). [ 6 ]
Second, the suppressed information is provided. The inclusion of the suppressed information is guided by the proof of a scheduling theorem due to Brent, [2] which is explained later in this article. The WT framework is useful since while it can greatly simplify the initial description of a parallel algorithm, inserting the details suppressed by ...
For this recurrence relation, the master theorem for divide-and-conquer recurrences gives the asymptotic bound () = (). It follows that, for sufficiently large n , Karatsuba's algorithm will perform fewer shifts and single-digit additions than longhand multiplication, even though its basic step uses more additions and shifts than the ...
The bracket integration method (method of brackets) applies Ramanujan's master theorem to a broad range of integrals. [7] The bracket integration method generates the integrand's series expansion , creates a bracket series, identifies the series coefficient and formula parameters and computes the integral.