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Lopsided shift-splitting preconditioner for saddle point problems with three-by-three structure

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Abstract

In this paper, a new preconditioner that combines the lopsided idea with the shift technique is proposed for the saddle point problem with three-by-three structure. The new preconditioner has computational advantages to implement within Krylov subspace acceleration. The convergence properties of the iteration method and the spectral distribution of the corresponding preconditioned matrix are analyzed. Numerical results show that the proposed new preconditioner is competitive with some existing preconditioners studied recently.

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Acknowledgements

The authors sincerely thank the Editor and referees for their valuable and detailed comments, suggestions and help, which led to a substantial improvement on the presentation and contents of this paper. The authors are partially supported by NSF of China (No. 11771259), special support program to develop innovative talents in the region of Shaanxi province, innovation team on computationally efficient numerical methods based on new energy problems in Shaanxi province, innovative team project of Shaanxi Provincial Department of Education (No. 21JP013), Natural Science Basic Research Program of Shaanxi Province (No. 2021JQ-526), Natural Science Foundation of Shaanxi Provincial Department of Education (No. 21JK0552).

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Authors and Affiliations

  1. School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an, 710021, People’s Republic of China

    Na Zhang, Rui-Xia Li & Jian Li

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  1. Na Zhang
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  2. Rui-Xia Li
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  3. Jian Li
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Contributions

Na Zhang: Software, Visualization, Data Curation, Writing - original draft. Rui-Xia Li: Conceptualization, Methodology, Writing-review & editing, Funding Acquisition. Jian Li: Conceptualization, Funding Acquisition, Resources, Supervision.

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Correspondence to Rui-Xia Li or Jian Li.

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Communicated by Gabriel Haeser.

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Zhang, N., Li, RX. & Li, J. Lopsided shift-splitting preconditioner for saddle point problems with three-by-three structure. Comp. Appl. Math. 41, 261 (2022). https://doi.org/10.1007/s40314-022-01944-w

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  • DOI: https://doi.org/10.1007/s40314-022-01944-w

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