TY - JOUR
T1 - Two Minimal Residual NHSS Iteration Methods for Complex Symmetric Linear Systems
AU - Wang , Yikang
AU - Zhang , Pingping
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 904
EP - 924
PY - 2025
DA - 2025/05
SN - 7
DO - http://doi.org/10.12150/jnma.2025.904
UR - https://global-sci.org/intro/article_detail/jnma/24108.html
KW - Complex symmetric linear systems, minimal residual technique,
inexact versions, convergence properties.
AB - <p style="text-align: justify;">For the large sparse complex symmetric linear systems, by applying the minimal residual technique to accelerate a preconditioned variant
of new Hermitian and skew-Hermitian splitting (${\rm P}^∗{\rm NHSS}$) method and efficient parameterized ${\rm P}^∗{\rm NHSS}$ $({\rm PPNHSS})$ method, we construct the minimal
residual ${\rm P}^∗{\rm NHSS}$ $({\rm MRP}^∗{\rm NHSS})$ method and the minimal residual ${\rm PPNHSS}$ $({\rm MRPPNHSS})$ method. The convergence properties of the two iteration methods are studied. Theoretical analyses imply that the ${\rm MRP}^∗{\rm NHSS}$ method
and the ${\rm MRPPNHSS}$ method converge unconditionally to the unique solution. In addition, we also give the inexact versions of ${\rm MRP}^∗{\rm NHSS}$ method
and ${\rm MRPPNHSS}$ method and their convergence proofs. Finally, numerical
experiments show the high efficiency and robustness of our methods.</p>