Krylov methods for solving linear systems

Krylov methods are considered as one of the most popular classes of numerical methods to solve large sparse linear systems of equations. One of the reasons for their popularity is that they are relatively simple to implement. Therefore, Krylov methods have been increasingly accepted as efficient and reliable alternative to the more expensive numerical methods. The purpose of this report is to describe the general concepts used in Krylov methods and to introduce different kinds of Krylov methods. This report also introduces a few simple preconditioners used with Krylov methods. Some C++ codes and Matlab plots are also included.