I came up with this algorithm for matrix multiplication. I read somewhere that matrix multiplication has a time complexity of o(n^2). But I think my this algorithm will give o(n^3). I don't know how to calculate time complexity of nested loops. So please correct me.
for i=1 to n
for j=1 to n
c[i][j]=0
for k=1 to n
c[i][j] = c[i][j]+a[i][k]*b[k][j]
This question is related to
algorithm
time-complexity
matrix-multiplication
The standard way of multiplying an m-by-n matrix by an n-by-p matrix has complexity O(mnp). If all of those are "n" to you, it's O(n^3), not O(n^2). EDIT: it will not be O(n^2) in the general case. But there are faster algorithms for particular types of matrices -- if you know more you may be able to do better.
In matrix multiplication there are 3 for loop, we are using since execution of each for loop requires time complexity O(n)
. So for three loops it becomes O(n^3)
Using linear algebra, there exist algorithms that achieve better complexity than the naive O(n3). Solvay Strassen algorithm achieves a complexity of O(n2.807) by reducing the number of multiplications required for each 2x2 sub-matrix from 8 to 7.
The fastest known matrix multiplication algorithm is Coppersmith-Winograd algorithm with a complexity of O(n2.3737). Unless the matrix is huge, these algorithms do not result in a vast difference in computation time. In practice, it is easier and faster to use parallel algorithms for matrix multiplication.
Source: Stackoverflow.com