Solving the Singular Semi-Sylvester Equation Using Drazin-Inverse and DGMRES Algorithm

Abstract

In this paper, we want to solve the singular semi-Sylvester equation using the Drazin-inverse andthe Drazin-inverse generalized minimum residual method (DGMRES (m) algorithm). First, we transform the semiSylvester equation into a multiple linear systems. Then, we present the conditions and assumptions needed to applythe DGMRES (m) algorithm. We compare our proposed method with the Galerkin projection method in point ofview CPU-time, accuracy and iteration number. Finally, by some numerical experiments, we show the efficiency ofthe proposed method.