IGMRES method for linear systems

The Index Generalized Minimal RESidual (IGMRES) algorithm is designed to compute the Drazin-inverse solution of a linear system of equations Ax = b, where A is an arbitrary square matrix with index γ. If γ = 0, then the this method method coincide with Generalized Minimal RESidual (GMRES) method. Also, the k th ideal index generalized minimal residual polynomial of A is introduced and the roots of these polynomials are studied. Moreover, by numerical results the con vergence rate of these methods are compared by two examples.