Two Minimal Residual NHSS Iteration Methods for Complex Symmetric Linear Systems (Journal of Nonlinear Modeling and Analysis, 2025)
For the large sparse complex symmetric linear systems, by applying the minimal residual technique to accelerate a preconditioned variantof new Hermitian and skew-Hermitian splitting (${\rm P}^∗{\rm NHSS}$) method and efficient parameterized ${\rm P}^∗{\rm NHSS}$ $({\rm PPNHSS})$ method, we construct the minimalresidual ${\rm P}^∗{\rm NHSS}$ $({\rm MRP}^∗{\rm NHSS})$ 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 ${\rm MRP}^∗{\rm NHSS}$ methodand the ${\rm MRPPNHSS}$ method converge unconditionally to the unique solution. In addition, we also give the inexact versions of ${\rm MRP}^∗{\rm NHSS}$ methodand ${\rm MRPPNHSS}$ method and their convergence proofs. Finally, numericalexperiments show the high efficiency and robustness of our methods.
Keywords: Complex symmetric linear systems; minimal residual technique; inexact versions; convergence properties.