This paper presents a new version of the successive approximations method for solving Sylvester equations AX − XB = C, where A and B are symmetric negative and positive definite matrices, respectively. This method is based on the block GMRES...

residual the block CMRH method cannot break down. Finally, some numerical examples

are presented to show the efficiency of the new method in comparison with the traditional

CMRH method and a comparison with the block GMRES method is also provided...