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The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem. The time for such an algorithm can be expressed ...
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.
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 transform of an analytic function; MacMahon master theorem (MMT), in enumerative combinatorics and linear algebra; Glasser's master theorem in integral calculus
Structured program theorem (computer science) Sturm's theorem (theory of equations) Sturm–Picone comparison theorem (differential equations) Subspace theorem (Diophantine approximation) Supersymmetry nonrenormalization theorems ; Supporting hyperplane theorem (convex geometry) Swan's theorem (module theory) Sylow theorems (group theory)
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 ...
In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, [1] is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem. The result is stated as follows:
D. Foata and G.-N. Han, A new proof of the Garoufalidis-Lê-Zeilberger Quantum MacMahon Master Theorem, Journal of Algebra 307 (2007), no. 1, 424–431 . D. Foata and G.-N. Han, Specializations and extensions of the quantum MacMahon Master Theorem, Linear Algebra and its Applications 423 (2007), no. 2–3, 445–455 .
recursion theorem 1. Master theorem (analysis of algorithms) 2. Kleene's recursion theorem recursive definition A definition of a function, set, or other mathematical object that is defined in terms of itself, using a base case and a rule for generating subsequent elements. recursive function
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