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Volume 7, Issue 3
Two Minimal Residual NHSS Iteration Methods for Complex Symmetric Linear Systems

Yikang Wang & Pingping Zhang

J. Nonl. Mod. Anal., 7 (2025), pp. 904-924.

Published online: 2025-05

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-904, author = {Wang , Yikang and Zhang , Pingping}, title = {Two Minimal Residual NHSS Iteration Methods for Complex Symmetric Linear Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {3}, pages = {904--924}, abstract = {

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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.904}, url = {http://global-sci.org/intro/article_detail/jnma/24108.html} }
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 -

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.

Wang , Yikang and Zhang , Pingping. (2025). Two Minimal Residual NHSS Iteration Methods for Complex Symmetric Linear Systems. Journal of Nonlinear Modeling and Analysis. 7 (3). 904-924. doi:10.12150/jnma.2025.904
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