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A least squares approach for saddle point problems

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Abstract

Saddle point linear systems arise in many applications in computational sciences and engineering such as finite element approximations to Stokes problems, image reconstructions, tomography, genetics, statistics, and model order reductions for dynamical systems. In this paper, we present a least-squares approach to solve saddle point linear systems. The basic idea is to construct a projection matrix and transform a given saddle point linear system to a least-squares problem and then solve the least-squares problem by an iterative method such as LSMR: an iterative method for sparse least-squares problems. The proposed method rivals LSMR applied to the original problem in simplicity and ease to use. Numerical experiments demonstrate that the new iterative method is efficient and converges fast

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Acknowledgements

The authors would like to thank the anonymous referees for their constructive comments and suggestions that improve the paper.

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Authors and Affiliations

  1. Vocational School of Health Services, Karamanoglu Mehmetbey University, Karaman, 70200, Turkey

    Gul Karaduman

  2. Department of Mathematics, University of Texas at Arlington, Arlington, TX, 76019-0408, USA

    Mei Yang & Ren-Cang Li

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  1. Gul Karaduman
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  2. Mei Yang
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  3. Ren-Cang Li
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Correspondence to Gul Karaduman.

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Supported in part by NSF grants DMS-1719620 and DMS-2009689.

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Karaduman, G., Yang, M. & Li, RC. A least squares approach for saddle point problems. Japan J. Indust. Appl. Math. 40, 95–107 (2023). https://doi.org/10.1007/s13160-022-00509-y

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  • DOI: https://doi.org/10.1007/s13160-022-00509-y

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