Global-DGMRES method for matrix equation AXB = C

Abstract

In this paper, we present a new algorithm Global-DGMRES to find the Drazin inverse solution of the linear matrix equation AXB = C, where at least one of the matrices A or B is rank deficient. This method is based on oblique projection process, onto matrix Krylov subspaces. Also, we study convergence properties of this algorithm. The matrix equation AXB = C is a mathematical model for deblurring problems and the Global-DGMRES method helps us to reconstruct blurred images corresponding to this matrix equation. Moreover, by numerical results, we compare the proposed method with Global-LSMR and Global-LSQR.

Keywords:

• Matrix equations
• global-DGMRES method
• drazin inverse solution
• matrix Krylov subspaces
• deblurring problems

2010 AMS SUBJECT CLASSIFICATIONS:

• 65F10
• 15A09

Disclosure statement

No potential conflict of interest was reported by the author(s).