Abstract
In order to find the least squares solution of minimal norm to linear system \(Ax=b\) with \(A \in \mathcal{C}^{m \times n}\) being a matrix of rank \(r< n \le m\), \(b \in \mathcal{C}^{m}\), Zheng and Wang (Appl Math Comput 169:1305–1323, 2005) proposed a class of symmetric successive overrelaxation (SSOR) methods, which is based on augmenting system to a block \(4 \times 4\) consistent system. In this paper, we construct the unsymmetric successive overrelaxation (USSOR) method. The semiconvergence of the USSOR method is discussed. Numerical experiments illustrate that the number of iterations and CPU time for the USSOR method with the appropriate parameters is respectively less and faster than the SSOR method with optimal parameters.
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Acknowledgments
The authors would like to thank the anonymous referees for their helpful comments and suggestions, which bring the authors’ attention to the references [5–7, 9] and greatly improve the original manuscript. This work is supported by the National Natural Science Foundation of China under Grant 11271196 and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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Song, J., Song, Y. USSOR methods for solving the rank deficient linear least squares problem. Calcolo 54, 95–115 (2017). https://doi.org/10.1007/s10092-016-0178-z
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DOI: https://doi.org/10.1007/s10092-016-0178-z