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The name "master theorem" was popularized by the widely used algorithms textbook Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein. Not all recurrence relations can be solved by this theorem; its generalizations include the Akra–Bazzi method.
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 ...
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 ...
Pages in category "Recurrence relations" The following 31 pages are in this category, out of 31 total. ... Master theorem (analysis of algorithms) Matrix difference ...
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 recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
In the most balanced case, a single quicksort call involves O(n) work plus two recursive calls on lists of size n/2, so the recurrence relation is = + (). The master theorem for divide-and-conquer recurrences tells us that T(n) = O(n log n).
The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology.It defines a large number of terms relating to algorithms and data structures.