Block DGMRES Algorithm for the Drazin-Inverse Solution of Singular Nonsymmetric Linear System with Multiple Right-Hand Sides

Many problems in science and engineering fields require the Drazin-inverse solution of singular linear systems with multiple right hand sides. To solve these systems efficiently, a block GMRES-like algorithm is derived. The new method can deal with consistent or inconsistent singular system with arbitrary index. Numerical experiments confirm the efficiency of our method.