> n = 3; A = rand(n,n); > flops(0); x = gauss_elim(A,b); flops ans = 60 > max(abs(A*x-b)) ans = 1.1102e-016 > x = rand(n,1); flops(0); [x,diffs] = jacobi(A,b,x,tol); flops ans = 533 > max(abs(A*x-b)) ans = 3.3307e-016 > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 248 > max(abs(A*x-b)) ans = 5.5511e-017 > n = 5; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > flops(0); x = gauss_elim(A,b); flops ans = 193 > flops(0); [x,diffs] = jacobi(A,b,x,tol); flops ans = 2092 > n = 5; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 766 > n = 10; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > flops(0); x = gauss_elim(A,b); flops ans = 1068 > x = rand(n,1); flops(0); [x,diffs] = jacobi(A,b,x,tol); flops ans = 7639 > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 3217 > n = 20; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > flops(0); x = gauss_elim(A,b); flops ans = 6843 > x = rand(n,1); flops(0); [x,diffs] = jacobi(A,b,x,tol); flops ans = 38449 > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 13618 > n = 30; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > flops(0); x = gauss_elim(A,b); flops ans = 21318 > x = rand(n,1); flops(0); [x,diffs] = jacobi(A,b,x,tol); flops ans = 86449 > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 30618 > n = 50; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > flops(0); x = gauss_elim(A,b); flops ans = 92368 > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 85018 > n = 100; A = rand(n,n); b = rand(n,1); for i=1:n, A(i,i) = n+A(i,i); end > flops(0); x = gauss_elim(A,b); flops ans = 702243 > x = rand(n,1); flops(0); [x,diffs] = gauss_seidel(A,b,x,tol); flops ans = 340018 From this, we see that gauss seidel becomes faster than direct gaussian elimination when the matrix gets big enough. Jacobi iteration never becomes uesful.