Akra–Bazzi method

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

The Akra–Bazzi method applies to recurrence formulas of the form

The conditions for usage are:

The asymptotic behavior of ${\displaystyle T(x)}$ is found by determining the value of ${\displaystyle p}$ for which ${\displaystyle \sum _{i=1}^{k}a_{i}b_{i}^{p}=1}$ and plugging that value into the equation

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