An iterative method for the bisymmetric solutions of the consistent matrix equations \(A_{1}XB_{1}=C_{1}, A_{2}XB_{2}=C_{2}\). (English) Zbl 1202.65052

Summary: An iterative method is presented for finding the bisymmetric solutions of a pair of consistent matrix equations \(A_{1}XB_{1}=C_{1}, A_{2}XB_{2}=C_{2}\), by which a bisymmetric solution can be obtained in finite iteration steps in the absence of round-off errors. Moreover, the solution with least Frobenius norm can be obtained by choosing a special kind of initial matrix. In the solution set of the matrix equations, the optimal approximation bisymmetric solution to a given matrix can also be derived by this iterative method. The efficiency of the proposed algorithm is shown by some numerical examples.


65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
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[1] Ben-Israel A., Generalized Inverse: Theory and Applications (2002)
[2] Bhimasankaram P., Sankhya Ser. A 38 pp 404– (1976)
[3] DOI: 10.1002/nla.496 · Zbl 1174.65382 · doi:10.1002/nla.496
[4] DOI: 10.1016/0024-3795(88)90223-6 · Zbl 0649.65026 · doi:10.1016/0024-3795(88)90223-6
[5] DOI: 10.1137/0131050 · Zbl 0359.65033 · doi:10.1137/0131050
[6] DOI: 10.1016/0024-3795(84)90166-6 · Zbl 0543.15011 · doi:10.1016/0024-3795(84)90166-6
[7] DOI: 10.1016/0024-3795(90)90377-O · Zbl 0712.15010 · doi:10.1016/0024-3795(90)90377-O
[8] DOI: 10.1016/S0898-1221(00)00330-8 · Zbl 0983.15016 · doi:10.1016/S0898-1221(00)00330-8
[9] DOI: 10.1016/j.amc.2006.01.071 · Zbl 1115.65048 · doi:10.1016/j.amc.2006.01.071
[10] DOI: 10.1016/j.laa.2007.05.034 · Zbl 1123.15009 · doi:10.1016/j.laa.2007.05.034
[11] DOI: 10.1002/nla.333 · Zbl 1164.15322 · doi:10.1002/nla.333
[12] DOI: 10.1017/S0305004100030929 · doi:10.1017/S0305004100030929
[13] DOI: 10.1016/j.amc.2006.12.026 · Zbl 1133.65026 · doi:10.1016/j.amc.2006.12.026
[14] Yuan Y. X., Math. Numer. Sinica 23 pp 429– (2001)
[15] Yuan Y. X., J. East China Shipbuilding Inst. 18 pp 29– (2004)
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