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  2. Master theorem (analysis of algorithms) - Wikipedia

    en.wikipedia.org/wiki/Master_theorem_(analysis...

    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 ...

  3. Akra–Bazzi method - Wikipedia

    en.wikipedia.org/wiki/Akra–Bazzi_method

    It is a generalization of the master theorem for divide-and-conquer recurrences, which assumes that the sub-problems have equal size. It is named after mathematicians Mohamad Akra and Louay Bazzi. It is named after mathematicians Mohamad Akra and Louay Bazzi.

  4. Category:Recurrence relations - Wikipedia

    en.wikipedia.org/wiki/Category:Recurrence_relations

    Download as PDF; Printable version; ... Pages in category "Recurrence relations" ... Master theorem (analysis of algorithms)

  5. Divide-and-conquer eigenvalue algorithm - Wikipedia

    en.wikipedia.org/wiki/Divide-and-conquer_eigen...

    W will use the master theorem for divide-and-conquer recurrences to analyze the running time. Remember that above we stated we choose n ≈ m / 2 {\displaystyle n\approx m/2} . We can write the recurrence relation :

  6. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    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)

  7. Merge sort - Wikipedia

    en.wikipedia.org/wiki/Merge_sort

    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]

  8. Recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Recurrence_relation

    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.

  9. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    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 ...