How many multiplications and divisions are required for one

How many multiplications and divisions are required for one iteration of the Gauss-Seidel method? How many iterations may be performed before th\'is number exceeds the operations count of Gauss elimination?

Solution

For the n set of linearly independent equations, we need to perform

n(n-1) multiplications and n divisions for each iterations

that scales well for higher value of n, since the other algorithm takes a fixed time equal to n^3/3 for finding the correct answer

Now let us assume the gauss-seidel method runs for k iterations we get

kn^2 > n(n-1)(2n-1)/6

Hence the value of k must be greater than n/3 in order to have more iterations then the regular method