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 \gamma. If \gamma=۰, 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 convergence rate of these methods are compared by two examples.

کلیدواژه ها:

Singular systems ، Drazin inverse ، DGMRES ، GMRES