Jia, Zhigang; Zhao, Linlin; Zhao, Meixiang Hermitian polynomial matrix equations and applications. (English) Zbl 07806661 Moslehian, Mohammad Sal (ed.), Matrix and operator equations and applications. Cham: Springer. Math. Online First Collect., 347-371 (2023). MSC: 15A24 47A62 47J05 47H14 65F45 PDFBibTeX XMLCite \textit{Z. Jia} et al., in: Matrix and operator equations and applications. Cham: Springer. 347--371 (2023; Zbl 07806661) Full Text: DOI
Li, Chang-Zhou Fixed point iterative methods for solving the nonlinear matrix equation \(X-A^*X^{-n}A=I\). (English) Zbl 1522.15017 J. Appl. Math. Comput. 69, No. 2, 1731-1749 (2023). MSC: 15A24 65F45 47H10 PDFBibTeX XMLCite \textit{C.-Z. Li}, J. Appl. Math. Comput. 69, No. 2, 1731--1749 (2023; Zbl 1522.15017) Full Text: DOI
Valencia, Carlos E.; Villagrán, Ralihe R. Arithmetical structures on dominated polynomials. (English) Zbl 07713856 São Paulo J. Math. Sci. 17, No. 1, 430-439 (2023). MSC: 11D72 11Y50 11C20 15B48 PDFBibTeX XMLCite \textit{C. E. Valencia} and \textit{R. R. Villagrán}, São Paulo J. Math. Sci. 17, No. 1, 430--439 (2023; Zbl 07713856) Full Text: DOI arXiv
Erfanifar, Raziyeh; Sayevand, Khosro; Hajarian, Masoud Solving system of nonlinear matrix equations over Hermitian positive definite matrices. (English) Zbl 07683826 Linear Multilinear Algebra 71, No. 4, 597-630 (2023). MSC: 15A24 15B57 65F45 PDFBibTeX XMLCite \textit{R. Erfanifar} et al., Linear Multilinear Algebra 71, No. 4, 597--630 (2023; Zbl 07683826) Full Text: DOI
Shil, Sourav; Nashine, Hemant Kumar; Soleymani, Fazlollah On an inversion-free algorithm for the nonlinear matrix problem \(\mathcal{X}^\alpha+ \mathcal{A}^\ast \mathcal{X}^{-\beta}\mathcal{A}+ \mathcal{B}^\ast \mathcal{X}^{- \gamma}\mathcal{B}=\mathcal{I}\). (English) Zbl 1513.65121 Int. J. Comput. Math. 99, No. 12, 2555-2567 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. Shil} et al., Int. J. Comput. Math. 99, No. 12, 2555--2567 (2022; Zbl 1513.65121) Full Text: DOI
Bai, Dongjian; Wang, Feng An \(\mathcal{H}\)-tensor-based criteria for testing the positive definiteness of multivariate homogeneous forms. (English) Zbl 1500.15018 Open Math. 20, 505-516 (2022). MSC: 15A69 15A18 65F15 65H17 PDFBibTeX XMLCite \textit{D. Bai} and \textit{F. Wang}, Open Math. 20, 505--516 (2022; Zbl 1500.15018) Full Text: DOI
Valencia, Carlos E.; Villagrán, Ralihe R. Algorithmic aspects of arithmetical structures. (English) Zbl 1493.11077 Linear Algebra Appl. 640, 191-208 (2022). Reviewer: Scott Corry (Appleton) MSC: 11D72 11Y50 11C20 15B48 PDFBibTeX XMLCite \textit{C. E. Valencia} and \textit{R. R. Villagrán}, Linear Algebra Appl. 640, 191--208 (2022; Zbl 1493.11077) Full Text: DOI arXiv
Liu, Lixia; Li, Xinyi; Liu, Sanyang Further study on existence and uniqueness of positive solution for tensor equations. (English) Zbl 1480.15016 Appl. Math. Lett. 124, Article ID 107686, 7 p. (2022). MSC: 15A24 15A69 PDFBibTeX XMLCite \textit{L. Liu} et al., Appl. Math. Lett. 124, Article ID 107686, 7 p. (2022; Zbl 1480.15016) Full Text: DOI
Bai, Dongjian; Wang, Feng New methods based \(\mathcal{H}\)-tensors for identifying the positive definiteness of multivariate homogeneous forms. (English) Zbl 1525.15018 AIMS Math. 6, No. 9, 10281-10295 (2021). MSC: 15A69 65F15 65H17 PDFBibTeX XMLCite \textit{D. Bai} and \textit{F. Wang}, AIMS Math. 6, No. 9, 10281--10295 (2021; Zbl 1525.15018) Full Text: DOI
Mousavi, Z.; Mirzapour, F. Applying solvability theorems for matrix equations. (English) Zbl 1484.15015 Oper. Matrices 15, No. 2, 685-692 (2021). MSC: 15A24 PDFBibTeX XMLCite \textit{Z. Mousavi} and \textit{F. Mirzapour}, Oper. Matrices 15, No. 2, 685--692 (2021; Zbl 1484.15015) Full Text: DOI
Hasanov, Vejdi I. Positive definite solutions of a linearly perturbed matrix equation. (English) Zbl 1499.65145 Ann. Acad. Rom. Sci., Math. Appl. 13, No. 1-2, 5-19 (2021). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{V. I. Hasanov}, Ann. Acad. Rom. Sci., Math. Appl. 13, No. 1--2, 5--19 (2021; Zbl 1499.65145) Full Text: Link
Guo, Xiao-Xia; Wu, Hong-Xiao Two structure-preserving-doubling like algorithms to solve the positive definite solution of the equation \(X-A^{\mathrm{H}}\overline{X}^{-1}A=Q\). (English) Zbl 1476.65065 Commun. Appl. Math. Comput. 3, No. 1, 123-135 (2021). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{X.-X. Guo} and \textit{H.-X. Wu}, Commun. Appl. Math. Comput. 3, No. 1, 123--135 (2021; Zbl 1476.65065) Full Text: DOI
Wang, Xuezhong; Mo, Changxin; Che, Maolin; Wei, Yimin Accelerated dynamical approaches for finding the unique positive solution of \(\mathcal{KS}\)-tensor equations. (English) Zbl 1482.65060 Numer. Algorithms 88, No. 4, 1787-1810 (2021). MSC: 65F15 65F10 15A69 PDFBibTeX XMLCite \textit{X. Wang} et al., Numer. Algorithms 88, No. 4, 1787--1810 (2021; Zbl 1482.65060) Full Text: DOI
Zhang, Juan; Li, Shifeng On the Hermitian positive definite solution and Newton’s method for a nonlinear matrix equation. (English) Zbl 1475.15019 Linear Multilinear Algebra 69, No. 11, 2093-2114 (2021). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{S. Li}, Linear Multilinear Algebra 69, No. 11, 2093--2114 (2021; Zbl 1475.15019) Full Text: DOI
Jin, Zhixiang; Zhai, Chengbo Investigation of positive definite solution of nonlinear matrix equation \(X^p=Q+\sum \nolimits_{i=1}^m A_i^*X^{\delta}A_i\). (English) Zbl 1476.15028 Comput. Appl. Math. 40, No. 3, Paper No. 74, 14 p. (2021). MSC: 15A24 47H10 PDFBibTeX XMLCite \textit{Z. Jin} and \textit{C. Zhai}, Comput. Appl. Math. 40, No. 3, Paper No. 74, 14 p. (2021; Zbl 1476.15028) Full Text: DOI
Masoudi, Mohsen; Salemi, Abbas On Hermitian positive definite solutions of a nonlinear matrix equation. (English) Zbl 1470.15013 J. Fixed Point Theory Appl. 23, No. 2, Paper No. 30, 19 p. (2021). MSC: 15A24 15B57 PDFBibTeX XMLCite \textit{M. Masoudi} and \textit{A. Salemi}, J. Fixed Point Theory Appl. 23, No. 2, Paper No. 30, 19 p. (2021; Zbl 1470.15013) Full Text: DOI
Zhai, Chengbo; Jin, Zhixiang Solvability for two forms of nonlinear matrix equations. (English) Zbl 1471.15011 Bull. Iran. Math. Soc. 47, No. 4, 1107-1120 (2021). MSC: 15A24 47H10 65F45 PDFBibTeX XMLCite \textit{C. Zhai} and \textit{Z. Jin}, Bull. Iran. Math. Soc. 47, No. 4, 1107--1120 (2021; Zbl 1471.15011) Full Text: DOI
Huang, Jingpin; Zhang, Shanshan; Xiong, Hao Iterative methods of the positive definite solution to a quadratic quaternion system. (Chinese. English summary) Zbl 1474.65075 Math. Appl. 34, No. 2, 357-364 (2021). MSC: 65F10 15B33 PDFBibTeX XMLCite \textit{J. Huang} et al., Math. Appl. 34, No. 2, 357--364 (2021; Zbl 1474.65075)
Gupta, Animesh; Rai, Vandana Binary relation for tripled fixed point theorem in metric spaces. (English) Zbl 1488.54135 Bol. Soc. Parana. Mat. (3) 39, No. 2, 9-26 (2021). MSC: 54H25 15A24 54E40 PDFBibTeX XMLCite \textit{A. Gupta} and \textit{V. Rai}, Bol. Soc. Parana. Mat. (3) 39, No. 2, 9--26 (2021; Zbl 1488.54135) Full Text: Link
Novak, Tina; Žerovnik, Janez Real forms of the complex Neumann system: a method for finding real roots of polynomial \(U_{\mathcal{S}} ( \lambda )\). (English) Zbl 1457.37079 J. Comput. Appl. Math. 390, Article ID 113362, 14 p. (2021). MSC: 37J39 37J35 15A06 26C10 PDFBibTeX XMLCite \textit{T. Novak} and \textit{J. Žerovnik}, J. Comput. Appl. Math. 390, Article ID 113362, 14 p. (2021; Zbl 1457.37079) Full Text: DOI arXiv
Huang, Baohua; Ma, Changfeng Some accelerated iterative algorithms for solving nonsymmetric algebraic Riccati equations arising in transport theory. (English) Zbl 1480.65098 Int. J. Comput. Math. 97, No. 9, 1819-1839 (2020). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, Int. J. Comput. Math. 97, No. 9, 1819--1839 (2020; Zbl 1480.65098) Full Text: DOI
Ivanov, Ivelin Georgiev; Tanov, Vladislav Krasimirov A nonsymmetric Nash-Riccati equation and decoupled schemes for a stabilizing solution. (English) Zbl 1467.65039 Appl. Math. E-Notes 20, 357-366 (2020). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{I. G. Ivanov} and \textit{V. K. Tanov}, Appl. Math. E-Notes 20, 357--366 (2020; Zbl 1467.65039) Full Text: Link
Meng, Jie; Lee, Hosoo; Kim, Hyun-Min On the extreme solutions of a class of nonlinear matrix equation. (English) Zbl 1464.15024 J. Nonlinear Convex Anal. 21, No. 1, 77-87 (2020). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{J. Meng} et al., J. Nonlinear Convex Anal. 21, No. 1, 77--87 (2020; Zbl 1464.15024) Full Text: Link
Rajasingam, Prasanthan; Xu, Jianhong On the convergence of the accelerated Riccati iteration method. (English) Zbl 1453.65085 Int. J. Control 93, No. 8, 1800-1809 (2020). MSC: 65F45 15A24 15B48 PDFBibTeX XMLCite \textit{P. Rajasingam} and \textit{J. Xu}, Int. J. Control 93, No. 8, 1800--1809 (2020; Zbl 1453.65085) Full Text: DOI arXiv
Hasanov, Vejdi I. Perturbation bounds for the matrix equation \(X + A^\ast X^{-1}A=Q\). (English) Zbl 1451.15011 Appl. Comput. Math. 19, No. 1, 20-33 (2020). MSC: 15A24 47H14 65H05 PDFBibTeX XMLCite \textit{V. I. Hasanov}, Appl. Comput. Math. 19, No. 1, 20--33 (2020; Zbl 1451.15011) Full Text: arXiv Link
Liu, Xifu; Luo, Le Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm. (English) Zbl 1442.15037 Appl. Math. Lett. 107, Article ID 106408, 7 p. (2020). MSC: 15A60 15A03 15A45 65F55 PDFBibTeX XMLCite \textit{X. Liu} and \textit{L. Luo}, Appl. Math. Lett. 107, Article ID 106408, 7 p. (2020; Zbl 1442.15037) Full Text: DOI
Chen, Haibin; Wang, Yiju; Zhou, Guanglu High-order sum-of-squares structured tensors: theory and applications. (English) Zbl 1439.65069 Front. Math. China 15, No. 2, 255-284 (2020). MSC: 65H17 15A18 90C30 PDFBibTeX XMLCite \textit{H. Chen} et al., Front. Math. China 15, No. 2, 255--284 (2020; Zbl 1439.65069) Full Text: DOI
Liu, Jianzhou; Zhang, Juan; Luo, Fangfang Newton’s method for the positive solution of the coupled algebraic Riccati equation applied to automatic control. (English) Zbl 1463.65092 Comput. Appl. Math. 39, No. 2, Paper No. 113, 17 p. (2020). MSC: 65F45 15A24 93E20 PDFBibTeX XMLCite \textit{J. Liu} et al., Comput. Appl. Math. 39, No. 2, Paper No. 113, 17 p. (2020; Zbl 1463.65092) Full Text: DOI
Ramadan, Mohamed A.; El-Shazly, Naglaa M. On the perturbation analysis of the maximal solution for the matrix equation \(X - \sum\limits_{i=1}^m A_i^\ast X^{-1} A_i + \sum\limits_{j=1}^n B_j^\ast X^{-1} B_j = I\). (English) Zbl 1434.15013 J. Egypt. Math. Soc. 28, Paper No. 6, 13 p. (2020). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{M. A. Ramadan} and \textit{N. M. El-Shazly}, J. Egypt. Math. Soc. 28, Paper No. 6, 13 p. (2020; Zbl 1434.15013) Full Text: DOI
Wu, Guoxing; Xing, Ting; Zhou, Duanmei Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation. (English) Zbl 1499.15056 Filomat 33, No. 9, 2667-2671 (2019). MSC: 15A24 15A42 PDFBibTeX XMLCite \textit{G. Wu} et al., Filomat 33, No. 9, 2667--2671 (2019; Zbl 1499.15056) Full Text: DOI
Huang, Baohua; Ma, Changfeng Some iterative algorithms for positive definite solution to nonlinear matrix equations. (English) Zbl 1490.65079 J. Appl. Anal. Comput. 9, No. 2, 526-546 (2019). MSC: 65F45 15A24 65H10 PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, J. Appl. Anal. Comput. 9, No. 2, 526--546 (2019; Zbl 1490.65079) Full Text: DOI
Mansouri, Mahmoud; Nassiri, Kameleh Positivity of continuous time irregular linear descriptor systems. (English) Zbl 1432.93125 Turk. J. Math. 43, No. 5, 2161-2169 (2019). MSC: 93C05 93C28 15B48 PDFBibTeX XMLCite \textit{M. Mansouri} and \textit{K. Nassiri}, Turk. J. Math. 43, No. 5, 2161--2169 (2019; Zbl 1432.93125) Full Text: Link
Kim, Taehyeong; Seo, Sang-Hyup; Kim, Hyun-Min On Newton’s method for solving a system of nonlinear matrix equations. (English) Zbl 1434.65045 East Asian Math. J. 35, No. 3, 341-349 (2019). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 65F45 65H10 15A24 PDFBibTeX XMLCite \textit{T. Kim} et al., East Asian Math. J. 35, No. 3, 341--349 (2019; Zbl 1434.65045) Full Text: DOI
Miao, Yun; Li, Chaoqian; Wei, Yimin Z-singular value and Z-singular value inclusion sets for tensors. (English) Zbl 1426.15010 Japan J. Ind. Appl. Math. 36, No. 3, 1055-1087 (2019). MSC: 15A18 15A69 65F10 65H10 65N22 PDFBibTeX XMLCite \textit{Y. Miao} et al., Japan J. Ind. Appl. Math. 36, No. 3, 1055--1087 (2019; Zbl 1426.15010) Full Text: DOI
Cai, Jing; Chen, Jianlong Some new bound estimates of the Hermitian positive definite solutions of the nonlinear matrix equation \({X^s} + {A^*}{X^{- t}}A = Q\). (English) Zbl 1438.15033 J. Southeast Univ., Engl. Ed. 35, No. 1, 142-146 (2019). MSC: 15A24 15A45 65F45 PDFBibTeX XMLCite \textit{J. Cai} and \textit{J. Chen}, J. Southeast Univ., Engl. Ed. 35, No. 1, 142--146 (2019; Zbl 1438.15033) Full Text: DOI
Wang, Xuezhong; Che, Maolin; Wei, Yimin Existence and uniqueness of positive solution for \(\mathcal{H}^+\)-tensor equations. (English) Zbl 1450.15026 Appl. Math. Lett. 98, 191-198 (2019). MSC: 15A69 15A24 65F45 PDFBibTeX XMLCite \textit{X. Wang} et al., Appl. Math. Lett. 98, 191--198 (2019; Zbl 1450.15026) Full Text: DOI
Fang, Liang; Liu, Sanyang On positive definite solution of a class of nonlinear matrix equations. (Chinese. English summary) Zbl 1438.15035 J. Zhejiang Univ., Sci. Ed. 46, No. 1, 1-8 (2019). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{L. Fang} and \textit{S. Liu}, J. Zhejiang Univ., Sci. Ed. 46, No. 1, 1--8 (2019; Zbl 1438.15035)
Li, Jing; Zhang, Yuhai The investigation on two kinds of nonlinear matrix equations. (English) Zbl 1425.15011 Bull. Malays. Math. Sci. Soc. (2) 42, No. 6, 3323-3341 (2019). Reviewer: Vladimir P. Kostov (Nice) MSC: 15A24 15A42 PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. Zhang}, Bull. Malays. Math. Sci. Soc. (2) 42, No. 6, 3323--3341 (2019; Zbl 1425.15011) Full Text: DOI
Liang, Wenting; Deng, Chunyuan The solutions to some operator equations with corresponding operators not necessarily having closed ranges. (English) Zbl 1502.47020 Linear Multilinear Algebra 67, No. 8, 1606-1624 (2019). MSC: 47A62 15A09 47A05 PDFBibTeX XMLCite \textit{W. Liang} and \textit{C. Deng}, Linear Multilinear Algebra 67, No. 8, 1606--1624 (2019; Zbl 1502.47020) Full Text: DOI
Wang, Feng; Sun, Deshu; Xu, Yumei Some criteria for identifying \(\mathcal{H}\)-tensors and its applications. (English) Zbl 1417.15035 Calcolo 56, No. 2, Paper No. 19, 17 p. (2019). MSC: 15A69 15A18 15A45 65F15 65H17 PDFBibTeX XMLCite \textit{F. Wang} et al., Calcolo 56, No. 2, Paper No. 19, 17 p. (2019; Zbl 1417.15035) Full Text: DOI
Du, Shouqiang; Zhang, Liping A mixed integer programming approach to the tensor complementarity problem. (English) Zbl 1425.90072 J. Glob. Optim. 73, No. 4, 789-800 (2019). MSC: 90C11 15A69 PDFBibTeX XMLCite \textit{S. Du} and \textit{L. Zhang}, J. Glob. Optim. 73, No. 4, 789--800 (2019; Zbl 1425.90072) Full Text: DOI arXiv
Huang, Baohua; Ma, Changfeng Some criteria for identifying strong \( \mathcal{H} \)-tensors and its applications. (English) Zbl 1411.15016 Linear Multilinear Algebra 67, No. 6, 1146-1173 (2019). MSC: 15A69 15A18 65F15 65H17 PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, Linear Multilinear Algebra 67, No. 6, 1146--1173 (2019; Zbl 1411.15016) Full Text: DOI
Huang, Baohua; Ma, Changfeng Iterative criteria for identifying strong \(\mathcal{H}\)-tensors. (English) Zbl 1445.65017 J. Comput. Appl. Math. 352, 93-109 (2019). MSC: 65F99 15A69 15A18 65F15 65H17 PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, J. Comput. Appl. Math. 352, 93--109 (2019; Zbl 1445.65017) Full Text: DOI
Han, Lixing A continuation method for tensor complementarity problems. (English) Zbl 1409.90201 J. Optim. Theory Appl. 180, No. 3, 949-963 (2019). MSC: 90C33 15A69 65H20 PDFBibTeX XMLCite \textit{L. Han}, J. Optim. Theory Appl. 180, No. 3, 949--963 (2019; Zbl 1409.90201) Full Text: DOI arXiv
He, Zhuo-Heng Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving \(\phi\)-skew-Hermicity. (English) Zbl 1409.15017 Adv. Appl. Clifford Algebr. 29, No. 1, Paper No. 6, 31 p. (2019). Reviewer: Yansheng Wu (Nanjing) MSC: 15B33 15A23 15A24 15B48 15B57 PDFBibTeX XMLCite \textit{Z.-H. He}, Adv. Appl. Clifford Algebr. 29, No. 1, Paper No. 6, 31 p. (2019; Zbl 1409.15017) Full Text: DOI
Gumus, Mehmet; Xu, Jianhong On common \(\alpha\)-scalar Lyapunov solutions. (English) Zbl 1405.15026 Linear Algebra Appl. 563, 123-141 (2019). MSC: 15A45 15B48 34D20 37C75 93D05 PDFBibTeX XMLCite \textit{M. Gumus} and \textit{J. Xu}, Linear Algebra Appl. 563, 123--141 (2019; Zbl 1405.15026) Full Text: DOI
Miyajima, Shinya Verified computation for the Hermitian positive definite solution of the conjugate discrete-time algebraic Riccati equation. (English) Zbl 1417.65123 J. Comput. Appl. Math. 350, 80-86 (2019). MSC: 65F30 15A24 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 350, 80--86 (2019; Zbl 1417.65123) Full Text: DOI
Song, Guangjing; Yu, Shaowen Nonnegative definite and re-nonnegative definite solutions to a system of matrix equations with statistical applications. (English) Zbl 1427.15020 Appl. Math. Comput. 338, 828-841 (2018). MSC: 15A24 15A03 15A09 62H05 PDFBibTeX XMLCite \textit{G. Song} and \textit{S. Yu}, Appl. Math. Comput. 338, 828--841 (2018; Zbl 1427.15020) Full Text: DOI
Yu, Siting; Li, Chunmei; Duan, Xuefeng Nonmonotone spectral projection gradient method for solving generalized Lyapunov equations. (Chinese. English summary) Zbl 1438.65084 Chin. J. Eng. Math. 35, No. 6, 673-683 (2018). MSC: 65F45 15A24 15B57 PDFBibTeX XMLCite \textit{S. Yu} et al., Chin. J. Eng. Math. 35, No. 6, 673--683 (2018; Zbl 1438.65084) Full Text: DOI
Li, J.; Zhang, Y. H. Solvability for a nonlinear matrix equation. (English) Zbl 1407.15018 Bull. Iran. Math. Soc. 44, No. 5, 1171-1184 (2018). MSC: 15A24 15B48 PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. H. Zhang}, Bull. Iran. Math. Soc. 44, No. 5, 1171--1184 (2018; Zbl 1407.15018) Full Text: DOI
Bagherpour, Negin; Mahdavi-Amiri, Nezam A competitive error in variables approach and algorithms for finding positive definite solutions of linear systems of matrix equations. (English) Zbl 1451.65047 Al-Baali, Mehiddin (ed.) et al., Numerical analysis and optimization. Selected papers based on the presentations at the 4th international conference, NAO-IV, Muscat, Oman, January 2–5, 2017. Cham: Springer. Springer Proc. Math. Stat. 235, 45-66 (2018). MSC: 65F45 15A24 15B48 15B57 PDFBibTeX XMLCite \textit{N. Bagherpour} and \textit{N. Mahdavi-Amiri}, Springer Proc. Math. Stat. 235, 45--66 (2018; Zbl 1451.65047) Full Text: DOI
Huang, Bao-Hua; Ma, Chang-Feng Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation. (English) Zbl 1397.65048 Numer. Algorithms 79, No. 1, 153-178 (2018). MSC: 65F10 15A24 PDFBibTeX XMLCite \textit{B.-H. Huang} and \textit{C.-F. Ma}, Numer. Algorithms 79, No. 1, 153--178 (2018; Zbl 1397.65048) Full Text: DOI
Hasanov, Vejdi Ismailov On the matrix equation \(X+A^\ast X^{-1} A-B^\ast C^{-1} B=I\). (English) Zbl 1396.15013 Linear Multilinear Algebra 66, No. 9, 1783-1798 (2018). MSC: 15A24 65H05 PDFBibTeX XMLCite \textit{V. I. Hasanov}, Linear Multilinear Algebra 66, No. 9, 1783--1798 (2018; Zbl 1396.15013) Full Text: DOI
Li, Jing; Zhang, Yuhai A homotopy continuation method for solving a matrix equation. (English) Zbl 1392.15025 J. Korean Math. Soc. 55, No. 2, 327-342 (2018). MSC: 15A24 15B57 PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. Zhang}, J. Korean Math. Soc. 55, No. 2, 327--342 (2018; Zbl 1392.15025) Full Text: Link
Sáez, Meritxell; Feliu, Elisenda; Wiuf, Carsten Graphical criteria for positive solutions to linear systems. (English) Zbl 1388.15002 Linear Algebra Appl. 552, 166-193 (2018). MSC: 15A06 PDFBibTeX XMLCite \textit{M. Sáez} et al., Linear Algebra Appl. 552, 166--193 (2018; Zbl 1388.15002) Full Text: DOI arXiv
Huang, Na; Ma, Chang-Feng The structure-preserving doubling algorithms for positive definite solution to a system of nonlinear matrix equations. (English) Zbl 1387.65038 Linear Multilinear Algebra 66, No. 4, 827-839 (2018). MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{N. Huang} and \textit{C.-F. Ma}, Linear Multilinear Algebra 66, No. 4, 827--839 (2018; Zbl 1387.65038) Full Text: DOI
Lin, Matthew M.; Chiang, Chun-Yueh An accelerated technique for solving one type of discrete-time algebraic Riccati equations. (English) Zbl 1390.39071 J. Comput. Appl. Math. 338, 91-110 (2018). MSC: 39B12 39B42 47J22 65H05 15A24 PDFBibTeX XMLCite \textit{M. M. Lin} and \textit{C.-Y. Chiang}, J. Comput. Appl. Math. 338, 91--110 (2018; Zbl 1390.39071) Full Text: DOI arXiv
Masoudi, Mohsen; Moghadam, Mahmoud Mohseni; Salemi, Abbas Hermitian positive definite solutions of the matrix equation \({{X^s}+{A^*}{X^{-t}}A=Q}\). (English) Zbl 1401.65047 J. Korean Math. Soc. 54, No. 6, 1667-1682 (2017). MSC: 65F30 15A24 15B48 47H10 PDFBibTeX XMLCite \textit{M. Masoudi} et al., J. Korean Math. Soc. 54, No. 6, 1667--1682 (2017; Zbl 1401.65047) Full Text: DOI
Zhang, Xindong; Feng, Xinlong The Hermitian positive definite solution of the nonlinear matrix equation. (English) Zbl 1401.15014 Int. J. Nonlinear Sci. Numer. Simul. 18, No. 5, 293-301 (2017). MSC: 15A24 15B48 65F30 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{X. Feng}, Int. J. Nonlinear Sci. Numer. Simul. 18, No. 5, 293--301 (2017; Zbl 1401.15014) Full Text: DOI
Ling, Yonghui; Xu, Xiubin On one-parameter family of Newton-like iterations for solving nonsymmetric algebraic Riccati equation from transport theory. (English) Zbl 1446.65026 J. Nonlinear Convex Anal. 18, No. 10, 1833-1848 (2017). MSC: 65H10 65F45 15A24 PDFBibTeX XMLCite \textit{Y. Ling} and \textit{X. Xu}, J. Nonlinear Convex Anal. 18, No. 10, 1833--1848 (2017; Zbl 1446.65026) Full Text: Link
Miyajima, Shinya Fast verified computation for solutions of algebraic Riccati equations arising in transport theory. (English) Zbl 1438.65080 Numer. Linear Algebra Appl. 24, No. 5, e2098, 12 p. (2017). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. Miyajima}, Numer. Linear Algebra Appl. 24, No. 5, e2098, 12 p. (2017; Zbl 1438.65080) Full Text: DOI
Ziętak, Krystyna From the strict Chebyshev approximant of a vector to the strict spectral approximant of a matrix. (English) Zbl 1421.65010 Zemánek, Jaroslav (ed.) et al., Études opératorielles. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 112, 307-346 (2017). Reviewer: Michael Jung (Dresden) MSC: 65F30 65F20 65F35 15A60 15A18 15B57 47A58 41A65 41A36 49J52 PDFBibTeX XMLCite \textit{K. Ziętak}, Banach Cent. Publ. 112, 307--346 (2017; Zbl 1421.65010) Full Text: DOI Link
Chen, Haibin; Huang, Zheng-Hai; Qi, Liqun Copositivity detection of tensors: theory and algorithm. (English) Zbl 1377.65060 J. Optim. Theory Appl. 174, No. 3, 746-761 (2017). Reviewer: Anton Iliev (Plovdiv) MSC: 65H17 15A18 90C30 15A69 PDFBibTeX XMLCite \textit{H. Chen} et al., J. Optim. Theory Appl. 174, No. 3, 746--761 (2017; Zbl 1377.65060) Full Text: DOI arXiv
Chiang, Chun-Yueh An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations. (English) Zbl 1373.93147 J. Franklin Inst. 354, No. 15, 7088-7118 (2017). MSC: 93C10 93B40 15A24 PDFBibTeX XMLCite \textit{C.-Y. Chiang}, J. Franklin Inst. 354, No. 15, 7088--7118 (2017; Zbl 1373.93147) Full Text: DOI
Han, Lixing A homotopy method for solving multilinear systems with M-tensors. (English) Zbl 1375.65060 Appl. Math. Lett. 69, 49-54 (2017). MSC: 65F30 65H20 15A69 PDFBibTeX XMLCite \textit{L. Han}, Appl. Math. Lett. 69, 49--54 (2017; Zbl 1375.65060) Full Text: DOI arXiv
Rajesh Kannan, M. \(P\)-proper splittings. (English) Zbl 1377.15005 Aequationes Math. 91, No. 4, 619-633 (2017). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 15A09 65F10 65F20 PDFBibTeX XMLCite \textit{M. Rajesh Kannan}, Aequationes Math. 91, No. 4, 619--633 (2017; Zbl 1377.15005) Full Text: DOI
Góra, Michał Some methods of construction of a common Lyapunov solution to a finite set of complex systems. (English) Zbl 1368.15018 Linear Algebra Appl. 530, 77-93 (2017). MSC: 15A45 15B48 34D20 93D05 93D09 93D30 PDFBibTeX XMLCite \textit{M. Góra}, Linear Algebra Appl. 530, 77--93 (2017; Zbl 1368.15018) Full Text: DOI
Fang, Liang; Liu, Sanyang; Yin, Xiaoyan Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations. (English) Zbl 1362.15008 J. Appl. Math. Comput. 53, No. 1-2, 245-269 (2017). Reviewer: Jaydeb Sarkar (Bangalore) MSC: 15A24 65F10 65F30 PDFBibTeX XMLCite \textit{L. Fang} et al., J. Appl. Math. Comput. 53, No. 1--2, 245--269 (2017; Zbl 1362.15008) Full Text: DOI
Du, Yongqiang; Feng, Wenying; Wang, Ying; Zhang, Guang Positive solutions for a nonlinear algebraic system with nonnegative coefficient matrix. (English) Zbl 1368.15013 Appl. Math. Lett. 64, 150-155 (2017). MSC: 15A24 47N40 60H10 PDFBibTeX XMLCite \textit{Y. Du} et al., Appl. Math. Lett. 64, 150--155 (2017; Zbl 1368.15013) Full Text: DOI
Ding, Weiyang; Wei, Yimin Solving multi-linear systems with \(\mathcal {M}\)-tensors. (English) Zbl 1371.65032 J. Sci. Comput. 68, No. 2, 689-715 (2016). MSC: 65F10 15A69 15B48 65F15 PDFBibTeX XMLCite \textit{W. Ding} and \textit{Y. Wei}, J. Sci. Comput. 68, No. 2, 689--715 (2016; Zbl 1371.65032) Full Text: DOI
Li, Chunmei; Duan, Xuefeng; Peng, Zhenyun; Jiang, Zhuling Positive definite solution of a class of generalized Lyapunov equation. (Chinese. English summary) Zbl 1374.65069 Pure Appl. Math. 32, No. 5, 505-514 (2016). MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{C. Li} et al., Pure Appl. Math. 32, No. 5, 505--514 (2016; Zbl 1374.65069) Full Text: DOI
Huang, Na; Ma, Changfeng; Tang, Jia The inversion-free iterative methods for a system of nonlinear matrix equations. (English) Zbl 1362.65057 Int. J. Comput. Math. 93, No. 9, 1470-1483 (2016). Reviewer: Edgar Pereira (Natal) MSC: 65H10 15A24 PDFBibTeX XMLCite \textit{N. Huang} et al., Int. J. Comput. Math. 93, No. 9, 1470--1483 (2016; Zbl 1362.65057) Full Text: DOI
El-Shazly, Naglaa M. On the perturbation estimates of the maximal solution for the matrix equation \(X + A^T \sqrt{X^{- 1}} A = P\). (English) Zbl 1441.15011 J. Egypt. Math. Soc. 24, No. 4, 644-649 (2016). MSC: 15A24 PDFBibTeX XMLCite \textit{N. M. El-Shazly}, J. Egypt. Math. Soc. 24, No. 4, 644--649 (2016; Zbl 1441.15011) Full Text: DOI
Gumus, Mehmet; Xu, Jianhong On common diagonal Lyapunov solutions. (English) Zbl 1382.93029 Linear Algebra Appl. 507, 32-50 (2016). MSC: 93D30 15A18 15A45 15B48 34D20 93D05 PDFBibTeX XMLCite \textit{M. Gumus} and \textit{J. Xu}, Linear Algebra Appl. 507, 32--50 (2016; Zbl 1382.93029) Full Text: DOI
Song, Yisheng; Qi, Liqun Tensor complementarity problem and semi-positive tensors. (English) Zbl 1349.90803 J. Optim. Theory Appl. 169, No. 3, 1069-1078 (2016). MSC: 90C33 15A69 PDFBibTeX XMLCite \textit{Y. Song} and \textit{L. Qi}, J. Optim. Theory Appl. 169, No. 3, 1069--1078 (2016; Zbl 1349.90803) Full Text: DOI arXiv
Mousavi, Z.; Mirzapour, F.; Moslehian, M. S. Positive definite solutions of certain nonlinear matrix equations. (English) Zbl 1342.15008 Oper. Matrices 10, No. 1, 113-126 (2016). Reviewer: Chen Sheng (Harbin) MSC: 15A24 PDFBibTeX XMLCite \textit{Z. Mousavi} et al., Oper. Matrices 10, No. 1, 113--126 (2016; Zbl 1342.15008) Full Text: DOI Link
Meng, Jie; Kim, Hyun-Min The positive definite solution to a nonlinear matrix equation. (English) Zbl 1343.65043 Linear Multilinear Algebra 64, No. 4, 653-666 (2016). Reviewer: Jaydeb Sarkar (Bangalore) MSC: 65F30 15A24 65F10 65H10 PDFBibTeX XMLCite \textit{J. Meng} and \textit{H.-M. Kim}, Linear Multilinear Algebra 64, No. 4, 653--666 (2016; Zbl 1343.65043) Full Text: DOI
Meng, Jie; Lee, Hyun-Jung; Kim, Hyun-Min Convergence of Newton’s method for solving a nonlinear matrix equation. (English) Zbl 1350.65047 East Asian Math. J. 32, No. 1, 013-025 (2016). Reviewer: Przemysław Stpiczyński (Lublin) MSC: 65H10 15A24 65F10 65F30 15B48 PDFBibTeX XMLCite \textit{J. Meng} et al., East Asian Math. J. 32, No. 1, 013--025 (2016; Zbl 1350.65047) Full Text: DOI
Li, Jian-Lei; Zhang, Li-Tao; Li, Xu-Dong; Li, Qing-Bin A modified Newton-Shamanskii method for a nonsymmetric algebraic Riccati equation. (English) Zbl 1334.49082 J. Comput. Anal. Appl. 21, No. 2, 380-393 (2016). MSC: 49M15 65H10 15A24 PDFBibTeX XMLCite \textit{J.-L. Li} et al., J. Comput. Anal. Appl. 21, No. 2, 380--393 (2016; Zbl 1334.49082)
Gao, Dongjie On Hermitian positive definite solutions of the nonlinear matrix equation \(X-A^{*}e^{X}A=I\). (English) Zbl 1330.65053 J. Appl. Math. Comput. 50, No. 1-2, 109-116 (2016). MSC: 65F10 15A24 PDFBibTeX XMLCite \textit{D. Gao}, J. Appl. Math. Comput. 50, No. 1--2, 109--116 (2016; Zbl 1330.65053) Full Text: DOI
Huang, Na; Ma, Chang-Feng Two structure-preserving-doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation. (English) Zbl 1443.65056 Comput. Math. Appl. 69, No. 6, 494-502 (2015). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{N. Huang} and \textit{C.-F. Ma}, Comput. Math. Appl. 69, No. 6, 494--502 (2015; Zbl 1443.65056) Full Text: DOI
Li, Lei; Wang, Qing-Wen; Shen, Shu-Qian On positive definite solutions of the nonlinear matrix equations \(X \pm A^* X^q A = Q\). (English) Zbl 1410.15030 Appl. Math. Comput. 271, 556-566 (2015). MSC: 15A24 65F30 65F35 65H10 PDFBibTeX XMLCite \textit{L. Li} et al., Appl. Math. Comput. 271, 556--566 (2015; Zbl 1410.15030) Full Text: DOI
Wang, Chuan-Long; Yan, Xi-Hong Parallel multisplitting methods with optimal weighting matrices for linear systems. (English) Zbl 1392.65076 Appl. Math. Comput. 259, 523-532 (2015). MSC: 65F10 65Y05 65F50 65N22 15B48 PDFBibTeX XMLCite \textit{C.-L. Wang} and \textit{X.-H. Yan}, Appl. Math. Comput. 259, 523--532 (2015; Zbl 1392.65076) Full Text: DOI
Asgari, Mohammad Sadegh; Mousavi, Baharak Solving a class of nonlinear matrix equations via the coupled fixed point theorem. (English) Zbl 1390.15047 Appl. Math. Comput. 259, 364-373 (2015). MSC: 15A24 47H10 65F30 65H10 54H25 PDFBibTeX XMLCite \textit{M. S. Asgari} and \textit{B. Mousavi}, Appl. Math. Comput. 259, 364--373 (2015; Zbl 1390.15047) Full Text: DOI
Berzig, Maher; Samet, Bessem Positive solution to a generalized Lyapunov equation via a coupled fixed point theorem in a metric space endowed with a partial order. (English) Zbl 1462.15020 Filomat 29, No. 8, 1831-1837 (2015). MSC: 15A24 15A29 47H10 PDFBibTeX XMLCite \textit{M. Berzig} and \textit{B. Samet}, Filomat 29, No. 8, 1831--1837 (2015; Zbl 1462.15020) Full Text: DOI
Guo, Chun-Hua; Yu, Bo A convergence result for matrix Riccati differential equations associated with \(m\)-matrices. (English) Zbl 1357.34034 Taiwanese J. Math. 19, No. 1, 77-89 (2015). MSC: 34A45 15B48 93C05 34D05 PDFBibTeX XMLCite \textit{C.-H. Guo} and \textit{B. Yu}, Taiwanese J. Math. 19, No. 1, 77--89 (2015; Zbl 1357.34034) Full Text: DOI
Hassanov, V.; Hakkaev, S. Newton’s method for a nonlinear matrix equation. (English) Zbl 1374.65067 C. R. Acad. Bulg. Sci. 68, No. 8, 973-982 (2015). Reviewer: Angela Slavova (Sofia) MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{V. Hassanov} and \textit{S. Hakkaev}, C. R. Acad. Bulg. Sci. 68, No. 8, 973--982 (2015; Zbl 1374.65067)
Otadi, M.; Mosleh, M. Minimal solution of fuzzy linear systems. (English) Zbl 1345.65022 Iran. J. Fuzzy Syst. 12, No. 1, 89-99 (2015). Reviewer: Józef Drewniak (Lancut) MSC: 65F20 15A06 15A09 15B48 15B15 65Y20 PDFBibTeX XMLCite \textit{M. Otadi} and \textit{M. Mosleh}, Iran. J. Fuzzy Syst. 12, No. 1, 89--99 (2015; Zbl 1345.65022) Full Text: Link
Yuan, Yongxin; Zuo, Kezheng The re-nonnegative definite and re-positive definite solutions to the matrix equation \(AXB=D\). (English) Zbl 1338.15038 Appl. Math. Comput. 256, 905-912 (2015). MSC: 15A24 PDFBibTeX XMLCite \textit{Y. Yuan} and \textit{K. Zuo}, Appl. Math. Comput. 256, 905--912 (2015; Zbl 1338.15038) Full Text: DOI
Yu, Bo; Dong, Ning; Wen, Feng-Hua; Chen, Xiao-Hong A hybrid iterative method for a class of Riccati equations in the critical case. (English) Zbl 1349.65149 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 77, No. 1, 21-34 (2015). MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{B. Yu} et al., Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 77, No. 1, 21--34 (2015; Zbl 1349.65149)
Huang, Na; Ma, Changfeng Two inversion-free iterative algorithms for computing the maximal positive definite solution of the nonlinear matrix equation. (English) Zbl 1330.65078 Appl. Comput. Math. 14, No. 2, 158-167 (2015). Reviewer: Anton Iliev (Plovdiv) MSC: 65H10 15A24 PDFBibTeX XMLCite \textit{N. Huang} and \textit{C. Ma}, Appl. Comput. Math. 14, No. 2, 158--167 (2015; Zbl 1330.65078) Full Text: Link
Liu, Xifu The Hermitian and nonnegative definite solutions of \(AX=B\) subject to \(CXC^{*} \geqslant D\). (English) Zbl 1338.15010 Math. Inequal. Appl. 18, No. 4, 1367-1374 (2015). Reviewer: Iveta Hnetynkova (Praha) MSC: 15A06 15A39 15B48 PDFBibTeX XMLCite \textit{X. Liu}, Math. Inequal. Appl. 18, No. 4, 1367--1374 (2015; Zbl 1338.15010) Full Text: DOI
Al-Dubiban, Asmaa M. On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\). (English) Zbl 1314.65062 J. Inequal. Appl. 2015, Paper No. 147, 18 p. (2015). MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{A. M. Al-Dubiban}, J. Inequal. Appl. 2015, Paper No. 147, 18 p. (2015; Zbl 1314.65062) Full Text: DOI
Asgari, Mohammad Sadegh; Mousavi, Baharak Coupled fixed point theorems with respect to binary relations in metric spaces. (English) Zbl 1527.54021 J. Nonlinear Sci. Appl. 8, No. 2, 153-162 (2015). MSC: 54H25 54E40 15A24 PDFBibTeX XMLCite \textit{M. S. Asgari} and \textit{B. Mousavi}, J. Nonlinear Sci. Appl. 8, No. 2, 153--162 (2015; Zbl 1527.54021) Full Text: DOI Link
Adam, Maria; Assimakis, Nicholas Nonrecursive solution for the discrete algebraic Riccati equation and \(X + \mathcal A^\ast X^{-1}\mathcal A=L\). (English) Zbl 1309.65046 Open Math. 13, 51-63 (2015). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{M. Adam} and \textit{N. Assimakis}, Open Math. 13, 51--63 (2015; Zbl 1309.65046) Full Text: DOI
Li, Jing; Zhang, Yuhai On the existence of positive definite solutions of a nonlinear matrix equation. (English) Zbl 1357.15008 Taiwanese J. Math. 18, No. 5, 1345-1364 (2014). MSC: 15A24 65F30 PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. Zhang}, Taiwanese J. Math. 18, No. 5, 1345--1364 (2014; Zbl 1357.15008) Full Text: DOI
Liu, Aijing; Chen, Guoliang On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + \sum_{i = 1}^m A_i^\ast X^{- t_i} A_i = Q\). (English) Zbl 1335.15019 Appl. Math. Comput. 243, 950-959 (2014). MSC: 15A24 PDFBibTeX XMLCite \textit{A. Liu} and \textit{G. Chen}, Appl. Math. Comput. 243, 950--959 (2014; Zbl 1335.15019) Full Text: DOI
Li, Zhao-Yan; Zhou, Bin; Lam, James Towards positive definite solutions of a class of nonlinear matrix equations. (English) Zbl 1334.15041 Appl. Math. Comput. 237, 546-559 (2014). MSC: 15A24 15B48 65F30 PDFBibTeX XMLCite \textit{Z.-Y. Li} et al., Appl. Math. Comput. 237, 546--559 (2014; Zbl 1334.15041) Full Text: DOI
Huang, Na; Ma, Chang Feng Some predictor-corrector-type iterative schemes for solving nonsymmetric algebraic Riccati equations arising in transport theory. (English) Zbl 1340.65074 Numer. Linear Algebra Appl. 21, No. 6, 761-780 (2014). Reviewer: Ninoslav Truhar (Osijek) MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{N. Huang} and \textit{C. F. Ma}, Numer. Linear Algebra Appl. 21, No. 6, 761--780 (2014; Zbl 1340.65074) Full Text: DOI
Li, Chao; Chen, Guanggui; Li, Mingming Solutions and perturbation estimates for matrix equation \(X-A^*X^{-q}A=Q\). (Chinese. English summary) Zbl 1324.65082 Numer. Math., Nanjing 36, No. 2, 97-107 (2014). MSC: 65H10 15A24 65F35 PDFBibTeX XMLCite \textit{C. Li} et al., Numer. Math., Nanjing 36, No. 2, 97--107 (2014; Zbl 1324.65082)