Example: Matrix Multiplication
	• We can compute C=AB recursively by dividing each matrix into 4 submatrices • The submatrices of A and B can be multiplied (using 8 multiplies of matrices of size n/2) • Resulting recurrence is T(n) = 8T(n/2) + O(n2) • Solution is T(n) = O(n3) • Strassen found a way to use just 7 multiplies of matrices of size n/2
					• Recurrence is T(n) = 7T(n/2) + O(n2) • Solution is T(n) = O(nlog 7) » O(n2.81) • The naive algorithm is better up to about n = 45 • Strassen’s Algorithm becomes faster than naive algorithm at about n = 120 • Current best bound for matrix multiply is O(n2.376)
			CS409 - Spring 2000					8