Ding, Wenxv; Liu, Zhihong; Li, Ying; Wei, Anli; Zhang, Mingcui New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems. (English) Zbl 07807003 Numer. Algorithms 95, No. 3, 1309-1323 (2024). MSC: 65F10 11R52 15A09 15A24 15B33 PDFBibTeX XMLCite \textit{W. Ding} et al., Numer. Algorithms 95, No. 3, 1309--1323 (2024; Zbl 07807003) Full Text: DOI
Li, Ying; Ding, Wenxu; Zhao, Xiaoyu; Wei, Anli; Zhao, Jianli Direct methods of solving quaternion matrix equation based on STP. (English) Zbl 07806658 Moslehian, Mohammad Sal (ed.), Matrix and operator equations and applications. Cham: Springer. Math. Online First Collect., 185-209 (2023). MSC: 15A24 47A62 15A69 15B33 PDFBibTeX XMLCite \textit{Y. Li} et al., in: Matrix and operator equations and applications. Cham: Springer. 185--209 (2023; Zbl 07806658) Full Text: DOI
Belkhiri, Radja; Guerarra, Sihem Some structures of submatrices in solution to the paire of matrix equations \(AX=C,XB=D\). (English) Zbl 07723663 Math. Found. Comput. 6, No. 2, 231-252 (2023). MSC: 15A24 15A09 15A03 PDFBibTeX XMLCite \textit{R. Belkhiri} and \textit{S. Guerarra}, Math. Found. Comput. 6, No. 2, 231--252 (2023; Zbl 07723663) Full Text: DOI
Hu, Jingjing; Ke, Yifen; Ma, Changfeng Efficient iterative method for generalized Sylvester quaternion tensor equation. (English) Zbl 07714795 Comput. Appl. Math. 42, No. 5, Paper No. 237, 26 p. (2023). MSC: 65F45 15A69 PDFBibTeX XMLCite \textit{J. Hu} et al., Comput. Appl. Math. 42, No. 5, Paper No. 237, 26 p. (2023; Zbl 07714795) Full Text: DOI
Fan, Xueling; Li, Ying; Sun, Jianhua; Zhao, Jianli Solving quaternion linear system \(AXB=E\) based on semi-tensor product of quaternion matrices. (English) Zbl 1507.15002 Banach J. Math. Anal. 17, No. 2, Paper No. 25, 20 p. (2023). MSC: 15A06 65F05 PDFBibTeX XMLCite \textit{X. Fan} et al., Banach J. Math. Anal. 17, No. 2, Paper No. 25, 20 p. (2023; Zbl 1507.15002) Full Text: DOI
Ding, Wenxv; Li, Ying; Wei, Anli Real representation for solving reduced biquaternion matrix equations \(XF - AX = BY\) and \(XF- A\widetilde{X} = BY\). (English) Zbl 07812732 Math. Methods Appl. Sci. 45, No. 17, 10532-10542 (2022). MSC: 11R52 15B33 65F05 65H10 PDFBibTeX XMLCite \textit{W. Ding} et al., Math. Methods Appl. Sci. 45, No. 17, 10532--10542 (2022; Zbl 07812732) Full Text: DOI
Sui, Yue; Huang, Yimin; Wei, Junchao Strongly EP elements and the solutions of equations in rings. (English) Zbl 1514.16036 Int. Electron. J. Algebra 32, 129-140 (2022). MSC: 16W10 16U99 15A09 PDFBibTeX XMLCite \textit{Y. Sui} et al., Int. Electron. J. Algebra 32, 129--140 (2022; Zbl 1514.16036) Full Text: Link
Wang, Qing-Wen; Lv, Ru-Yuan; Zhang, Yang The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra. (English) Zbl 1492.15017 Linear Multilinear Algebra 70, No. 10, 1942-1962 (2022). MSC: 15A69 15A24 15A10 PDFBibTeX XMLCite \textit{Q.-W. Wang} et al., Linear Multilinear Algebra 70, No. 10, 1942--1962 (2022; Zbl 1492.15017) Full Text: DOI
Zhang, Fengxia; Wei, Musheng; Li, Ying; Zhao, Jianli An efficient real representation method for least squares problem of the quaternion constrained matrix equation \(AXB + CY D = E\). (English) Zbl 1484.65080 Int. J. Comput. Math. 98, No. 7, 1408-1419 (2021). MSC: 65F45 15A24 15B33 PDFBibTeX XMLCite \textit{F. Zhang} et al., Int. J. Comput. Math. 98, No. 7, 1408--1419 (2021; Zbl 1484.65080) Full Text: DOI
Chen, Huaxi; Wang, Long; Li, Tingting A note on the solvability for generalized Sylvester equations. (English) Zbl 1460.15019 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 115, No. 2, Paper No. 64, 7 p. (2021). MSC: 15A24 15A06 15A09 PDFBibTeX XMLCite \textit{H. Chen} et al., Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 115, No. 2, Paper No. 64, 7 p. (2021; Zbl 1460.15019) Full Text: DOI
Liu, Xin; He, Zhuo-Heng \( \eta \)-Hermitian solution to a system of quaternion matrix equations. (English) Zbl 1452.15007 Bull. Malays. Math. Sci. Soc. (2) 43, No. 6, 4007-4027 (2020). MSC: 15A24 15A09 15B33 15B57 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Z.-H. He}, Bull. Malays. Math. Sci. Soc. (2) 43, No. 6, 4007--4027 (2020; Zbl 1452.15007) Full Text: DOI
Chapman, Adam Polynomial equations over octonion algebras. (English) Zbl 1450.17012 J. Algebra Appl. 19, No. 6, Article ID 2050102, 10 p. (2020). Reviewer: Ivan Kaygorodov (Novosibirsk) MSC: 17D05 15A18 15B33 PDFBibTeX XMLCite \textit{A. Chapman}, J. Algebra Appl. 19, No. 6, Article ID 2050102, 10 p. (2020; Zbl 1450.17012) Full Text: DOI arXiv
He, Zhuo-Heng; Wang, Meng; Liu, Xin On the general solutions to some systems of quaternion matrix equations. (English) Zbl 1436.15017 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114, No. 2, Paper No. 95, 22 p. (2020). MSC: 15A24 15A09 15B33 15B57 PDFBibTeX XMLCite \textit{Z.-H. He} et al., Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114, No. 2, Paper No. 95, 22 p. (2020; Zbl 1436.15017) Full Text: DOI
Liu, Xin; He, Zhuo-Heng On the split quaternion matrix equation \(AX=B\). (English) Zbl 1429.15028 Banach J. Math. Anal. 14, No. 1, 228-248 (2020). MSC: 15B33 15A24 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Z.-H. He}, Banach J. Math. Anal. 14, No. 1, 228--248 (2020; Zbl 1429.15028) Full Text: DOI
Ling, Si-Tao; Jia, Zhi-Gang; Lu, Xin; Yang, Bing Matrix LSQR algorithm for structured solutions to quaternionic least squares problem. (English) Zbl 1442.65102 Comput. Math. Appl. 77, No. 3, 830-845 (2019). MSC: 65K05 90C20 15A24 15B57 PDFBibTeX XMLCite \textit{S.-T. Ling} et al., Comput. Math. Appl. 77, No. 3, 830--845 (2019; Zbl 1442.65102) Full Text: DOI
Rehman, Abdur; Kyrchei, Ivan; Akram, Muhammad; Ali, Ilyas; Shakoor, Abdul Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations. (English) Zbl 1457.15017 Abstr. Appl. Anal. 2019, Article ID 9072690, 18 p. (2019). MSC: 15A24 15B33 PDFBibTeX XMLCite \textit{A. Rehman} et al., Abstr. Appl. Anal. 2019, Article ID 9072690, 18 p. (2019; Zbl 1457.15017) Full Text: DOI
Rehman, Abdur; Kyrchei, Ivan; Ali, Ilyas; Akram, Muhammad; Shakoor, Abdul The general solution of quaternion matrix equation having \(\eta \)-skew-Hermicity and its Cramer’s rule. (English) Zbl 1435.15013 Math. Probl. Eng. 2019, Article ID 7939238, 25 p. (2019). MSC: 15A24 15B33 PDFBibTeX XMLCite \textit{A. Rehman} et al., Math. Probl. Eng. 2019, Article ID 7939238, 25 p. (2019; Zbl 1435.15013) Full Text: DOI
Liu, Xin; Huang, Huajun; He, Zhuo-Heng Real representation approach to quaternion matrix equation involving \(\varphi \)-Hermicity. (English) Zbl 1435.15022 Math. Probl. Eng. 2019, Article ID 3258349, 8 p. (2019). MSC: 15B33 15A24 PDFBibTeX XMLCite \textit{X. Liu} et al., Math. Probl. Eng. 2019, Article ID 3258349, 8 p. (2019; Zbl 1435.15022) Full Text: DOI
He, Zhuo-Heng A system of coupled quaternion matrix equations with seven unknowns and its applications. (English) Zbl 1414.15021 Adv. Appl. Clifford Algebr. 29, No. 3, Paper No. 38, 24 p. (2019). MSC: 15A24 15B33 15B57 PDFBibTeX XMLCite \textit{Z.-H. He}, Adv. Appl. Clifford Algebr. 29, No. 3, Paper No. 38, 24 p. (2019; Zbl 1414.15021) Full Text: DOI
Kyrchei, Ivan I. Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation. (English) Zbl 1474.15041 Abstr. Appl. Anal. 2019, Article ID 5926832, 14 p. (2019). MSC: 15A24 15A15 15B57 15B33 PDFBibTeX XMLCite \textit{I. I. Kyrchei}, Abstr. Appl. Anal. 2019, Article ID 5926832, 14 p. (2019; Zbl 1474.15041) Full Text: DOI
Liu, Xin The \(\eta \)-anti-Hermitian solution to some classic matrix equations. (English) Zbl 1426.15021 Appl. Math. Comput. 320, 264-270 (2018). MSC: 15A24 15B33 15B57 PDFBibTeX XMLCite \textit{X. Liu}, Appl. Math. Comput. 320, 264--270 (2018; Zbl 1426.15021) Full Text: DOI
Wang, Qing-Wen; Yang, Xiao-Xiao; Yuan, Shi-Fang The least square solution with the least norm to a system of quaternion matrix equations. (English) Zbl 1397.15011 Iran. J. Sci. Technol., Trans. A, Sci. 42, No. 3, 1317-1325 (2018). MSC: 15A24 15A06 15A09 15B33 PDFBibTeX XMLCite \textit{Q.-W. Wang} et al., Iran. J. Sci. Technol., Trans. A, Sci. 42, No. 3, 1317--1325 (2018; Zbl 1397.15011) Full Text: DOI
Rehman, Abdur; Akram, Muhammad Optimization of a nonlinear Hermitian matrix expression with application. (English) Zbl 1488.15067 Filomat 31, No. 9, 2805-2819 (2017). MSC: 15B57 15A09 PDFBibTeX XMLCite \textit{A. Rehman} and \textit{M. Akram}, Filomat 31, No. 9, 2805--2819 (2017; Zbl 1488.15067) Full Text: DOI
He, Zhuo-Heng; Wang, Qing-Wen; Zhang, Yang Simultaneous decomposition of quaternion matrices involving \(\eta\)-Hermicity with applications. (English) Zbl 1411.15023 Appl. Math. Comput. 298, 13-35 (2017). MSC: 15B33 15A09 15A23 15A24 15B57 PDFBibTeX XMLCite \textit{Z.-H. He} et al., Appl. Math. Comput. 298, 13--35 (2017; Zbl 1411.15023) Full Text: DOI
Song, Guang-Jing; Yu, Shaowen The solution of a generalized Sylvester quaternion matrix equation and its application. (English) Zbl 1382.15024 Adv. Appl. Clifford Algebr. 27, No. 3, 2473-2492 (2017). MSC: 15A24 15B33 15A09 15B57 PDFBibTeX XMLCite \textit{G.-J. Song} and \textit{S. Yu}, Adv. Appl. Clifford Algebr. 27, No. 3, 2473--2492 (2017; Zbl 1382.15024) Full Text: DOI
Rehman, Abdur; Wang, Qing-Wen; Ali, Ilyas; Akram, Muhammad; Ahmad, M. O. A constraint system of generalized Sylvester quaternion matrix equations. (English) Zbl 1386.15035 Adv. Appl. Clifford Algebr. 27, No. 4, 3183-3196 (2017). MSC: 15A24 15A03 15A09 15B33 15B57 11R52 PDFBibTeX XMLCite \textit{A. Rehman} et al., Adv. Appl. Clifford Algebr. 27, No. 4, 3183--3196 (2017; Zbl 1386.15035) Full Text: DOI
Xu, Wei-Ru; Chen, Guo-Liang Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating. (English) Zbl 1443.15013 Comput. Math. Appl. 71, No. 5, 1074-1088 (2016). MSC: 15A29 PDFBibTeX XMLCite \textit{W.-R. Xu} and \textit{G.-L. Chen}, Comput. Math. Appl. 71, No. 5, 1074--1088 (2016; Zbl 1443.15013) Full Text: DOI
Yu, Juan; Shen, Shu-Qian Solvability of systems of linear matrix equations subject to a matrix inequality. (English) Zbl 1357.15009 Linear Multilinear Algebra 64, No. 12, 2446-2462 (2016). Reviewer: Andreas Arvanitoyeorgos (Patras) MSC: 15A24 15B57 15B48 15A03 15A45 PDFBibTeX XMLCite \textit{J. Yu} and \textit{S.-Q. Shen}, Linear Multilinear Algebra 64, No. 12, 2446--2462 (2016; Zbl 1357.15009) Full Text: DOI
Yuan, Shi-Fang; Wang, Qing-Wen L-structured quaternion matrices and quaternion linear matrix equations. (English) Zbl 1334.65075 Linear Multilinear Algebra 64, No. 2, 321-339 (2016). MSC: 65F30 65F10 15A24 15B33 PDFBibTeX XMLCite \textit{S.-F. Yuan} and \textit{Q.-W. Wang}, Linear Multilinear Algebra 64, No. 2, 321--339 (2016; Zbl 1334.65075) Full Text: DOI
Rehman, Abdur; Wang, Qing-Wen A system of matrix equations with five variables. (English) Zbl 1410.15033 Appl. Math. Comput. 271, 805-819 (2015). MSC: 15A24 11R52 15A09 15B57 PDFBibTeX XMLCite \textit{A. Rehman} and \textit{Q.-W. Wang}, Appl. Math. Comput. 271, 805--819 (2015; Zbl 1410.15033) Full Text: DOI
Ling, Si-Tao; Cheng, Xue-Han; Jiang, Tong-Song Consimilarity of quaternions and coneigenvalues of quaternion matrices. (English) Zbl 1410.15055 Appl. Math. Comput. 270, 984-992 (2015). MSC: 15B33 15A21 PDFBibTeX XMLCite \textit{S.-T. Ling} et al., Appl. Math. Comput. 270, 984--992 (2015; Zbl 1410.15055) Full Text: DOI
Ke, Yi-Fen; Ma, Chang-Feng Alternating direction method for generalized Sylvester matrix equation \(AXB + CYD = E\). (English) Zbl 1410.65123 Appl. Math. Comput. 260, 106-125 (2015). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{Y.-F. Ke} and \textit{C.-F. Ma}, Appl. Math. Comput. 260, 106--125 (2015; Zbl 1410.65123) Full Text: DOI
He, Zhuo-Heng; Wang, Qing-Wen The general solutions to some systems of matrix equations. (English) Zbl 1334.15040 Linear Multilinear Algebra 63, No. 10, 2017-2032 (2015). Reviewer: Rabe von Randow (Bonn) MSC: 15A24 15A09 15B33 15B57 PDFBibTeX XMLCite \textit{Z.-H. He} and \textit{Q.-W. Wang}, Linear Multilinear Algebra 63, No. 10, 2017--2032 (2015; Zbl 1334.15040) Full Text: DOI
Yuan, Shi-Fang; Liao, An-Ping; Wang, Peng Least squares {\(\eta\)}-bi-Hermitian problems of the quaternion matrix equation \((AXB,CXD) = (E,F)\). (English) Zbl 1328.65103 Linear Multilinear Algebra 63, No. 9, 1849-1863 (2015). Reviewer: Murli Gupta (Washington, D. C.) MSC: 65F30 15B33 65F20 15A24 PDFBibTeX XMLCite \textit{S.-F. Yuan} et al., Linear Multilinear Algebra 63, No. 9, 1849--1863 (2015; Zbl 1328.65103) Full Text: DOI
Hajarian, Masoud Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations. (English) Zbl 1321.65066 Comput. Appl. Math. 34, No. 2, 755-771 (2015). MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{M. Hajarian}, Comput. Appl. Math. 34, No. 2, 755--771 (2015; Zbl 1321.65066) Full Text: DOI
Yuan, Shi-Fang Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm. (English) Zbl 1442.15026 J. Appl. Math. 2014, Article ID 857081, 9 p. (2014). MSC: 15A24 15B33 PDFBibTeX XMLCite \textit{S.-F. Yuan}, J. Appl. Math. 2014, Article ID 857081, 9 p. (2014; Zbl 1442.15026) Full Text: DOI
Zhang, Yu-Ping; Dong, Chang-Zhou The \(^*\) congruence class of the solutions to a system of matrix equations. (English) Zbl 1442.15027 J. Appl. Math. 2014, Article ID 703529, 7 p. (2014). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{Y.-P. Zhang} and \textit{C.-Z. Dong}, J. Appl. Math. 2014, Article ID 703529, 7 p. (2014; Zbl 1442.15027) Full Text: DOI
Song, Guang-Jing Common solutions to some operator equations over Hilbert \(C^{\ast}\)-modules and applications. (English) Zbl 1315.47015 Linear Multilinear Algebra 62, No. 7, 895-912 (2014). Reviewer: Mohammad Sal Moslehian (Karlstad) MSC: 47A62 47B15 47B65 46L08 15A09 15A24 PDFBibTeX XMLCite \textit{G.-J. Song}, Linear Multilinear Algebra 62, No. 7, 895--912 (2014; Zbl 1315.47015) Full Text: DOI
Xiong, Zhiping Upper and lower bounds for ranks of the matrix expression \(X-XAX\). (English) Zbl 1291.15011 Abstr. Appl. Anal. 2013, Article ID 267035, 6 p. (2013). MSC: 15A09 90C20 PDFBibTeX XMLCite \textit{Z. Xiong}, Abstr. Appl. Anal. 2013, Article ID 267035, 6 p. (2013; Zbl 1291.15011) Full Text: DOI
Wang, QingWen; He, ZhuoHeng A system of matrix equations and its applications. (English) Zbl 1291.15043 Sci. China, Math. 56, No. 9, 1795-1820 (2013). Reviewer: Mihail Voicu (Iaşi) MSC: 15A24 15A09 15A03 PDFBibTeX XMLCite \textit{Q. Wang} and \textit{Z. He}, Sci. China, Math. 56, No. 9, 1795--1820 (2013; Zbl 1291.15043) Full Text: DOI
Zhang, Xiang; Xiang, Shu-Wen Solving optimization problems on Hermitian matrix functions with applications. (English) Zbl 1268.15016 J. Appl. Math. 2013, Article ID 593549, 11 p. (2013). MSC: 15A24 15A18 15A03 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{S.-W. Xiang}, J. Appl. Math. 2013, Article ID 593549, 11 p. (2013; Zbl 1268.15016) Full Text: DOI
Yu, Shao-Wen Ranks of a constrained Hermitian matrix expression with applications. (English) Zbl 1266.15028 J. Appl. Math. 2013, Article ID 514984, 9 p. (2013); erratum ibid. 2013, Article ID 826397, 1 p. (2013). MSC: 15B33 15A03 PDFBibTeX XMLCite \textit{S.-W. Yu}, J. Appl. Math. 2013, Article ID 514984, 9 p. (2013; Zbl 1266.15028) Full Text: DOI
Wang, Qing-Wen; Zhang, Xiang; He, Zhuo-Heng On the Hermitian structures of the solution to a pair of matrix equations. (English) Zbl 1264.15020 Linear Multilinear Algebra 61, No. 1, 73-90 (2013); corrigendum ibid. 61, No. 8, 1158 (2013). Reviewer: Ludwig Kohaupt (Berlin) MSC: 15A24 15A03 15A09 PDFBibTeX XMLCite \textit{Q.-W. Wang} et al., Linear Multilinear Algebra 61, No. 1, 73--90 (2013; Zbl 1264.15020) Full Text: DOI
He, Zhuo-Heng; Wang, Qing-Wen Solutions to optimization problems on ranks and inertias of a matrix function with applications. (English) Zbl 1309.15025 Appl. Math. Comput. 219, No. 6, 2989-3001 (2012). MSC: 15A24 15B57 PDFBibTeX XMLCite \textit{Z.-H. He} and \textit{Q.-W. Wang}, Appl. Math. Comput. 219, No. 6, 2989--3001 (2012; Zbl 1309.15025) Full Text: DOI
Wang, Qing-Wen; Yu, Juan Constrained solutions of a system of matrix equations. (English) Zbl 1268.15015 J. Appl. Math. 2012, Article ID 471573, 19 p. (2012). MSC: 15A24 65F30 15B10 15B57 PDFBibTeX XMLCite \textit{Q.-W. Wang} and \textit{J. Yu}, J. Appl. Math. 2012, Article ID 471573, 19 p. (2012; Zbl 1268.15015) Full Text: DOI
Dong, Chang-Zhou; Wang, Qing-Wen; Zhang, Yu-Ping On the Hermitian \(R\)-conjugate solution of a system of matrix equations. (English) Zbl 1268.15008 J. Appl. Math. 2012, Article ID 398085, 14 p. (2012). MSC: 15A24 65F30 PDFBibTeX XMLCite \textit{C.-Z. Dong} et al., J. Appl. Math. 2012, Article ID 398085, 14 p. (2012; Zbl 1268.15008) Full Text: DOI