The core of many equation solvers is a matrix
multiplication routine. The time complexity of calculating the matrix
product C=AB where A, B, and C are 
matrices, using traditional matrix multiplication, is 
. Strassen's matrix multiplication algorithm
is able to perform this
calculation in time 
[8, 15].
Thus one might be able to speed up the code by using Strassen's
algorithm instead of the traditional algorithm. Both IBM and Cray
support routines for fast matrix multiplications using Strassen's
algorithm. See also [2, 3] for examples of implementations of
Strassen's algorithm. However, the error bound given by Strassen's
algorithm is weaker than that of the traditional algorithm [5, 9]. Thus
the approaches might give different answers. If one suspects that this
is the case one can use comparative debugging to determine if and when
the result of Strassen's algorithm differs significantly from that of
the ordinary algorithm.
View example of Strassen' algorithm: 
,
or 
.