AOCL-Sparse Iterative Solver Suite (itsol) is an iterative framework for solving large-scale sparse linear systems of equations of the form
where \(A\) is a sparse full-rank square matrix of size \(n\) by \(n\), \(b\) is a dense \(n\)-vector, and \(x\) is the vector of unknowns also of size \(n\). The framework solves the previous problem using either the Conjugate Gradient method or GMRES. It supports a variety of preconditioners (accelerators) such as Symmetric Gauss-Seidel or Incomplete LU factorization, ILU(0).
Iterative solvers at each step (iteration) find a better approximation to the solution of the linear system of equations in the sense that it reduces an error metric. In contrast, direct solvers only provide a solution once the full algorithm as been executed. A great advantage of iterative solvers is that they can be interrupted once an approximate solution is deemed acceptable.