Let’s look at one more way to solve the equation . We assume that is nonsingular, and define the -th Krylov subspace as follows:
Krylov subspace methods are efficient and popular iterative methods for solving large, sparse linear systems. When is symmetric, positive definite (SPD), i.e.
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.