The main point of this paper is to solve 001336&_mathId=si1.gif&_user=111111111&_pii=S0168927415001336&_rdoc=1&_issn=01689274&md5=3da898365c374a996c273fdf469053f7" title="Click to view the MathML source">AX=B$AX=B$, where 001336&_mathId=si2.gif&_user=111111111&_pii=S0168927415001336&_rdoc=1&_issn=01689274&md5=6c1da35ea67d18b9148dedfcc37a1c02" title="Click to view the MathML source">X,B∈R^m×s$X,B\in R^{m\times s}$, for the first time by the presented methods.

Presenting deflated and augmented global OR, MR, MINRES, and GMRES type methods for solving matrix equations.

Bring a class of algorithms (Def-Aug-Global algorithm).

Reducing the number of iterations and CPU time in 5 examples in comparison with the global CG, MINRES and GMRES methods.

This work for interested people in solving matrix equation in all areas of science can be helpful.