Abstract
We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditioned matrix. Inexact variants are also considered. Numerical results on saddle-point linear systems arising from the discretization of a Stokes problem and of a distributed control problem show that good performance can be achieved when using inexact variants of the proposed preconditioners.
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Acknowledgments
The authors are very much indebted to Kang–Ya Lu for running the numerical results. They are also thankful to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of this paper.
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Communicated by Lars Eldén.
Supported by The National Natural Science Foundation for Creative Research Groups (No. 11321061) and The National Natural Science Foundation (No. 11671393), P.R. China, and by DOE (Office of Science) Grant ERKJ247.
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Bai, ZZ., Benzi, M. Regularized HSS iteration methods for saddle-point linear systems. Bit Numer Math 57, 287–311 (2017). https://doi.org/10.1007/s10543-016-0636-7
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DOI: https://doi.org/10.1007/s10543-016-0636-7
Keywords
- Saddle-point linear system
- Hermitian and skew-Hermitian splitting
- Iterative methods
- Inexact implementation
- Preconditioning
- Convergence