Flexible global generalized Hessenberg methods for linear systems with multiple right-hand sides

A variant of the global generalized Hessenberg method is presented which allows varying preconditioning at each restart. Theoretical results that relate the residual norm of this new method with its original version are developed. As two special variants, the flexible global GMRES method and the flexible global CMRH method are investigated both theoretically and experimentally. Numerical examples are conducted to illustrate the performance of these two flexible global methods in comparison with both the original global methods and weighted global methods.