For a non singular matrix $A$, solve $Ax=b$ for $x$. We introduce $x=A^Ty$ and obtain $AA^Ty=b$. Write out the Gauss-Seidel relation for $y$, $y+δe_i \to y$. Calculate $δ$.
Do I use $AA^Ty=b$ and then do $(L+D+U)A^Ty=b \to (L+D)(A^Ty)^{k+1}=b-U(A^Ty)^k$ and solve for $y^{k+1}$? What is $e_i$ here? Any hints would be appreciated