Krylov Subspace and GMRES Algorithm
In recent years, many fields have involved the problem of solving large-scale sparse systems of equations. When the problem size is extremely large, solving them becomes very difficult. Fortunately, Krylov subspace methods can handle such problems very well, and thus they have also been rated as one of the ten greatest algorithms of the 20th century. In this article, we will introduce the basic idea of the Krylov subspace and the famous GMRES algorithm (Generalized Minimal Residual Method).