  This study investigates the iterative regularization properties of two Krylov
methods for solving large-scale ill-posed problems: the changing minimal
residual Hessenberg method (CMRH) and a novel hybrid variant called the hybrid
changing minimal residual Hessenberg method (H-CMRH). Both methods share the
advantages of avoiding inner products, making them efficient and highly
parallelizable, and particularly suited for implementations that exploit
randomization and mixed precision arithmetic. Theoretical results and extensive
numerical experiments suggest that H-CMRH exhibits comparable performance to
the established hybrid GMRES method in terms of stabilizing semiconvergence,
but H-CMRH has does not require any inner products, and requires less work and
storage per iteration.
