H-CMRH: An Inner Product Free Hybrid Krylov Method for Large-Scale Inverse Problems
Ariana N. Brown, Malena Sabaté Landman, James G. Nagy · SIAM Journal on Matrix Analysis and Applications · 2025
Abstract. 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 new 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 low 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 does not require any inner products, and requires less work and storage per iteration.