Question

The problem: Compute AB, where A and B are both n×n matrices and n is a positive integer.

The algorithms: standard matrix multiplication algorithm; a simple recursive algorithm; Strassen’s algorithm.

Your task: Explain which of these three algorithms for this problem is fastest (asymptotically, in the worstcase). Explain how it achieves a performance increase over the other algorithms.

Answer 1

Computing AxB, where A and B are both n×n matrices and n is a positive integer.
standard matrix multiplication algorithm = O(n³)
simple recursive algorithm = O(n³)
Strassen’s algorithm =O(n^log7) = O(n^2.8074)
Therefore,Strassen’s algorithm for this problem is fastest

In simple recursive algorithm, the main component for high time complexity is 8 recursive calls.
Recurrence Relation
T(n) = 8*T(n/2) + O(n²)
on solving,Recurrence Relation we get Time complexity = O(n³)

But Strassen’s algorithm reduce the number of recursive calls to 7.
Recurrence Relation
T(n) = 7*T(n/2) + O(n²)
on solving,Recurrence Relation we get Time complexity = O(n^2.8074)