### Abstract

This article contains a formalisation of the Akra-Bazzi method based on a proof by Leighton. It is a generalisation of the well-known Master Theorem for analysing the complexity of Divide & Conquer algorithms. We also include a generalised version of the Master theorem based on the Akra-Bazzi theorem, which is easier to apply than the Akra-Bazzi theorem itself.

Some proof methods that facilitate applying the Master theorem are also included. For a more detailed explanation of the formalisation and the proof methods, see the accompanying paper (publication forthcoming).

### License

BSD License

### Topics

- Mathematics/Analysis

### Session Akra_Bazzi

- Akra_Bazzi_Library
- Akra_Bazzi_Asymptotics
- Akra_Bazzi_Real
- Akra_Bazzi
- Master_Theorem
- Eval_Numeral
- Akra_Bazzi_Method
- Akra_Bazzi_Approximation
- Master_Theorem_Examples

### Depends on

- Landau Symbols

### Used by

- Schönhage-Strassen Multiplication
- Karatsuba Multiplication on Integers
- Closest Pair of Points Algorithms

## Cite

×

Akra_Bazzi-AFP

    @article{Akra_Bazzi-AFP,
      author  = {Manuel Eberl},
      title   = {The Akra-Bazzi theorem and the Master theorem},
      journal = {Archive of Formal Proofs},
      month   = {July},
      year    = {2015},
      note    = {\url{https://isa-afp.org/entries/Akra_Bazzi.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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