Question

I want to multiply two matrices but the triple loop has O(n³) complexity. Is there any algorithm in dynamic programming to multiply two matrices with O(n) complexity?

ok fine we can’t get best than O(n^2.81 )

edit: but is there any solution that can even approximate the result upto some specific no. of columns and rows of matrix

i mean we get the best of O(n^2.81 ) with a complex solution but perfect results but if there is any solution for even an approximation of multiplication of matrices as we have formulas for factorial approximation etc.

if there is any you know it will help me

regards.

Answer 1

The best Matrix Multiplication Algorithm known so far is the “Coppersmith-Winograd algorithm” with O(n^2.38 ) complexity but it is not used for practical purposes.

However you can always use “Strassen’s algorithm” which has O(n^2.81 ) complexity but there is no such known algorithm for matrix multiplication with O(n) complexity.