Let’s look at one more way to solve the equation 
Krylov subspace methods are efficient and popular iterative methods for solving large, sparse linear systems. When 
![\left\{\begin{array}{l} A^{T} = A \\[12pt] \vec{x}^{T}A\vec{x} > 0,\,\,\,\forall\,\vec{x} \neq \vec{0}, \end{array}\right.](https://s0.wp.com/latex.php?latex=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D+A%5E%7BT%7D+%3D+A+%5C%5C%5B12pt%5D+%5Cvec%7Bx%7D%5E%7BT%7DA%5Cvec%7Bx%7D+%3E+0%2C%5C%2C%5C%2C%5C%2C%5Cforall%5C%2C%5Cvec%7Bx%7D+%5Cneq+%5Cvec%7B0%7D%2C+%5Cend%7Barray%7D%5Cright.&bg=ffffff&fg=1a1a1a&s=0 "\left\{\begin{array}{l} A^{T} = A \\[12pt] \vec{x}^{T}A\vec{x} > 0,\,\,\,\forall\,\vec{x} \neq \vec{0}, \end{array}\right.")
we can use a Krylov subspace method called Conjugate Gradient (CG).
Today, let’s find out how CG works and use it to solve 2D Poisson’s equation.
