Note to the convergence of minimum residual HSS method

The minimum residual hss (mrhss) method is proposed in [bit numerical mathematics, 59 (2019) 299--319] and its convergence analysis is proved under a certain condition. more recently in [appl. math. lett. 94 (2019) 210--216], an alternative version of mrhss is presented which converges unconditionally. in general, as the second approach works with a weighted inner product, it consumes more cpu time than mrhss to converge. in the current work, we revisit the convergence analysis of the mrhss method using a different strategy and state the convergence result for general two-step iterative schemes. it turns out that a special choice of parameters in the mrhss results in an unconditionally convergent method without using a weighted inner product. numerical experiments confirm the validity of established results.