We see from the above results that the Jacobi algorithm reduces the

error quite slowly in each iteration. For a general matrix of size n $\backslash$times n$,$

Gaussian elimination $($or Cholesky factorization$)$ costs O $($n$3)$ whereas

each iteration of Jacobi costs O $($n$2).$ So$,$ for a system of size n $=100,$

if we perform more than $100$ Jacobi iterations, we are doing more work

than the direct solvers $($Gaussian$/$Cholesky$)$ Ouch! However, we

now note that the matrix A has a special structure.