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Least squares solution of the quaternion matrix equation \(X-A\hat{X}B=C\) with the least norm. (English) Zbl 1228.65072

Consider the least squares solutions of the matrix equation \(X-AYB= C\) over the skew field of quaternions, where the matrices \(A,B\), and \(C\) are given and \(Y\) is the j-conjugate matrix of \(X\). By using the complex representation of the quaternion matrix and the Kronecker product of matrices, the concerned problems are turned into that of some real matrix equations. Then the authors derive the explicit expressions of the least squares solution with least norm, the least squares j-conjugate solution and the least squares anti j-conjugate solution

MSC:

65F30 Other matrix algorithms (MSC2010)
65F20 Numerical solutions to overdetermined systems, pseudoinverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A24 Matrix equations and identities
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References:

[1] DOI: 10.1016/j.laa.2006.06.005 · Zbl 1119.15014
[2] DOI: 10.1080/03081089508818358 · Zbl 0824.15015
[3] DOI: 10.1016/0024-3795(95)00090-9 · Zbl 0841.15007
[4] DOI: 10.1016/S0024-3795(02)00633-X · Zbl 1019.15002
[5] DOI: 10.1007/s10114-004-0428-x · Zbl 1083.15019
[6] Jiang TS, Acta Math. Sci. (China) 26 pp 578– (2006)
[7] DOI: 10.1016/j.camwa.2007.06.015 · Zbl 1143.15012
[8] DOI: 10.1080/03081088308817543 · Zbl 0527.15006
[9] DOI: 10.1016/j.mcm.2009.07.008 · Zbl 1185.15011
[10] DOI: 10.1016/j.amc.2007.05.021 · Zbl 1149.15011
[11] DOI: 10.1016/j.laa.2008.05.031 · Zbl 1158.15010
[12] DOI: 10.1016/j.amc.2006.12.039 · Zbl 1124.15010
[13] DOI: 10.1016/j.amc.2006.06.012 · Zbl 1108.15014
[14] DOI: 10.1016/j.amc.2007.05.018 · Zbl 1149.15012
[15] DOI: 10.1016/j.amc.2009.04.011 · Zbl 1176.15021
[16] DOI: 10.1016/j.mcm.2007.06.024 · Zbl 1145.15302
[17] DOI: 10.1016/j.cam.2009.01.013 · Zbl 1390.15055
[18] DOI: 10.1016/j.aml.2007.12.004 · Zbl 1221.65109
[19] DOI: 10.1016/j.mcm.2007.08.009 · Zbl 1145.15303
[20] DOI: 10.1016/0024-3795(95)00543-9 · Zbl 0873.15008
[21] DOI: 10.1016/j.mcm.2008.12.030 · Zbl 1185.15012
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