Note to the convergence of minimum residual HSS method

The minimum residual HSS (MRHSS) method is proposed in [BIT Numerical Mathematics, ۵۹ (۲۰۱۹) ۲۹۹--۳۱۹] and its convergence analysis is proved under a certain condition. More recently in [Appl. Math. Lett. ۹۴ (۲۰۱۹) ۲۱۰--۲۱۶], 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.

کلیدواژه ها:

Minimum residual technique ، Hermitian and skew-Hermitian splitting ، two-step iterative method ، Convergence