Peng, Zhen-Yun A matrix LSQR iterative method to solve matrix equation \(AXB=C\). (English) Zbl 1195.65056 Int. J. Comput. Math. 87, No. 8, 1820-1830 (2010). Summary: This paper is a matrix iterative method presented to compute the solutions of the matrix equation, \(AXB=C\), with unknown matrix \(X\in \mathcal S\), where \(\mathcal S\) is the constrained matrices set like symmetric, symmetric-\(R\)-symmetric and \((R, S)\)-symmetric. By this iterative method, for any initial matrix \(X_{0}\in S\), a solution \(X^*\) can be obtained within finite iteration steps if exact arithmetics were used, and the solution \(X^*\) with the minimum Frobenius norm can be obtained by choosing a special kind of initial matrix. The solution \(\hat X\), which is nearest to a given matrix \(\tilde X\) in Frobenius norm, can be obtained by first finding the minimum Frobenius norm solution of a new compatible matrix equation. The numerical examples given here show that the iterative method proposed in this paper has faster convergence and higher accuracy than the iterative methods proposed in earlier papers. Cited in 18 Documents MSC: 65F30 Other matrix algorithms (MSC2010) 65F10 Iterative numerical methods for linear systems Keywords:iterative method; LSQR algorithm; matrix equation; least-squares problem; matrix nearness problem Software:Mulprec PDFBibTeX XMLCite \textit{Z.-Y. Peng}, Int. J. Comput. Math. 87, No. 8, 1820--1830 (2010; Zbl 1195.65056) Full Text: DOI References: [1] DOI: 10.1016/0024-3795(89)90067-0 · Zbl 0688.15003 [2] G. Dahlquist and Å. Björck,Numerical Methods in Scientific Computing, Vol. II SIAM Member Price, 2008, pp. 507–508. Available at:http://www.mai.liu.se/ akbjo/NMbook.html [3] DOI: 10.1016/0024-3795(81)90290-1 · Zbl 0464.15006 [4] DOI: 10.1016/0024-3795(90)90370-R · Zbl 0712.15009 [5] DOI: 10.1137/0702016 · Zbl 0194.18201 [6] DOI: 10.1016/j.cam.2006.12.005 · Zbl 1146.65036 [7] DOI: 10.1016/j.amc.2006.10.011 · Zbl 1131.65038 [8] Liao A.-P., J. Comput. Math. 25 pp 543– (2007) [9] DOI: 10.1145/355984.355989 · Zbl 0478.65016 [10] Peng Z.-Y., J. Eng. Math. 6 pp 60– (2003) [11] DOI: 10.1016/j.amc.2004.12.032 · Zbl 1081.65039 [12] DOI: 10.1016/S0024-3795(03)00607-4 · Zbl 1050.15016 [13] Peng Y.-X., Appl. Math. Comput. 160 pp 763– (2005) · Zbl 1068.65056 [14] Toutounian F., Appl. Math. Comput. 178 pp 452– (2006) [15] DOI: 10.1016/j.laa.2004.01.018 · Zbl 1121.15016 [16] DOI: 10.1016/j.laa.2004.03.035 · Zbl 1059.15019 [17] Wang Q.-W., Comment. Math. Univ. Carolinae 39 pp 7– (1998) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.