Is there any method for multiplying matrices having O(n) complexity?

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?

Answer 1

Short answer: No

Long answer: There are ways if you have special kinds of matricies (for instance a diagonal matrix). The better matrix multiplication algorithms out there can pare you down to something like O(n^2.4) (http://en.wikipedia.org/wiki/Coppersmith-Winograd_algorithm). The major one I am somewhat familiar with uses a divide and conquer algorithm to split up the workload (not the one I linked to).

I hope this helps!