We are considering an iterative solution to the linear system
where is an
sparse matrix, x and
b are vectors of length N, and we are solving for x.
Iterative solvers are an alternative to direct methods that attempt to
calculate an exact solution to the system of equations. Iterative
methods attempt to find a solution to the system of linear equations
by repeatedly solving the linear system using approximations to the
vector. Iterations continue until the solution is within a
predetermined acceptable bound on the error.