Duan, Xuefeng; Li, Chunmei; Liao, Anping; Wang, Ronghao On two classes of mixed-type Lyapunov equations. (English) Zbl 1291.65136 Appl. Math. Comput. 219, No. 16, 8486-8495 (2013). MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{X. Duan} et al., Appl. Math. Comput. 219, No. 16, 8486--8495 (2013; Zbl 1291.65136) Full Text: DOI
Duan, Xuefeng; Wang, Qingwen; Liao, Anping On the matrix equation \(X-\sum^m_{i=1}N^\ast_iX^{-1}N_i=I\) arising in an interpolation problem. (English) Zbl 1288.15018 Linear Multilinear Algebra 61, No. 9, 1192-1205 (2013). Reviewer: João R. Cardoso (Coimbra) MSC: 15A24 65H10 65F30 PDFBibTeX XMLCite \textit{X. Duan} et al., Linear Multilinear Algebra 61, No. 9, 1192--1205 (2013; Zbl 1288.15018) Full Text: DOI
Yao, Guozhu; Liao, Anping; Duan, Xuefeng Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\). (English) Zbl 1214.15011 Numer. Algorithms 56, No. 3, 349-361 (2011). Reviewer: Constantin Popa (Constanţa) MSC: 15A24 15B48 PDFBibTeX XMLCite \textit{G. Yao} et al., Numer. Algorithms 56, No. 3, 349--361 (2011; Zbl 1214.15011) Full Text: DOI
Yao, Guozhu; Liao, Anping; Duan, Xuefeng Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{-\delta}A\). (English) Zbl 1207.15017 Electron. J. Linear Algebra 21, 76-84 (2010). MSC: 15A24 PDFBibTeX XMLCite \textit{G. Yao} et al., Electron. J. Linear Algebra 21, 76--84 (2010; Zbl 1207.15017) Full Text: DOI EuDML EMIS
Yao, Guozhu; Duan, Xuefeng; Liao, Anping Hermitian positive definite solution of the matrix equation \(X=Q+A^*(I_m\otimes X-C)^{-1}A\). (Chinese. English summary) Zbl 1224.15031 Pure Appl. Math. 26, No. 2, 257-261 (2010). MSC: 15A24 41A05 PDFBibTeX XMLCite \textit{G. Yao} et al., Pure Appl. Math. 26, No. 2, 257--261 (2010; Zbl 1224.15031)
Liao, An-Ping; Yao, Guo-Zhu; Duan, Xue-Feng Thompson metric method for solving a class of nonlinear matrix equation. (English) Zbl 1226.65034 Appl. Math. Comput. 216, No. 6, 1831-1836 (2010). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{A.-P. Liao} et al., Appl. Math. Comput. 216, No. 6, 1831--1836 (2010; Zbl 1226.65034) Full Text: DOI
Liu, Wei; Liao, Anping; Duan, Xuefeng Hermitian positive definite solutions of the matrix equation \(X+A^*X^{-q}A=Q\) \((q\geq 1)\). (English) Zbl 1212.65180 J. Math. Res. Expo. 29, No. 5, 831-838 (2009). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{W. Liu} et al., J. Math. Res. Expo. 29, No. 5, 831--838 (2009; Zbl 1212.65180) Full Text: DOI
Duan, Xuefeng; Liao, Anping; Peng, Zhenyun Positive definite solution of the matrix equation \(X-\sum^m_{i=1}A^*_iX^\delta A_i=Q\). (Chinese. English summary) Zbl 1212.65177 Chin. J. Eng. Math. 26, No. 4, 757-759 (2009). MSC: 65F30 15A24 47H07 PDFBibTeX XMLCite \textit{X. Duan} et al., Chin. J. Eng. Math. 26, No. 4, 757--759 (2009; Zbl 1212.65177)
Duan, Xuefeng; Liao, Anping On the nonlinear matrix equation \(X+A*X - qA=Q\) \((q\geq 1)\). (English) Zbl 1165.15302 Math. Comput. Modelling 49, No. 5-6, 936-945 (2009). MSC: 15A24 PDFBibTeX XMLCite \textit{X. Duan} and \textit{A. Liao}, Math. Comput. Modelling 49, No. 5--6, 936--945 (2009; Zbl 1165.15302) Full Text: DOI
Duan, Xuefeng; Liao, Anping On Hermitian positive definite solution of the matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q\). (English) Zbl 1170.15005 J. Comput. Appl. Math. 229, No. 1, 27-36 (2009). Reviewer: Sheng Chen (Harbin) MSC: 15A24 PDFBibTeX XMLCite \textit{X. Duan} and \textit{A. Liao}, J. Comput. Appl. Math. 229, No. 1, 27--36 (2009; Zbl 1170.15005) Full Text: DOI
Duan, Xuefeng; Liao, Anping The Hermitian positive definite solution of matrix equation \(X+A^*X^{-q}A=Q\) \((q\geq 1)\) and its perturbation analysis. (Chinese. English summary) Zbl 1174.15338 Numer. Math., Nanjing 30, No. 3, 280-288 (2008). MSC: 15A24 65F30 PDFBibTeX XMLCite \textit{X. Duan} and \textit{A. Liao}, Numer. Math., Nanjing 30, No. 3, 280--288 (2008; Zbl 1174.15338)
Liao, Anping; Duan, Xuefeng; Shen, Jinrong Hermitian positive definite solutions of the matrix equation \(X+A^*X^{-q}A=Q(q\geq 1)\). (Chinese. English summary) Zbl 1174.15343 Math. Numer. Sin. 30, No. 4, 369-378 (2008). MSC: 15A24 65F30 PDFBibTeX XMLCite \textit{A. Liao} et al., Math. Numer. Sin. 30, No. 4, 369--378 (2008; Zbl 1174.15343)
Duan, Xuefeng; Liao, Anping On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\). (English) Zbl 1143.15011 Linear Algebra Appl. 429, No. 4, 673-687 (2008). MSC: 15A24 15A42 PDFBibTeX XMLCite \textit{X. Duan} and \textit{A. Liao}, Linear Algebra Appl. 429, No. 4, 673--687 (2008; Zbl 1143.15011) Full Text: DOI
Duan, Xuefeng; Liao, Anping; Tang, Bin On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\). (English) Zbl 1148.15012 Linear Algebra Appl. 429, No. 1, 110-121 (2008). Reviewer: Qing-Wen Wang (Shanghai) MSC: 15A24 65F30 65H10 PDFBibTeX XMLCite \textit{X. Duan} et al., Linear Algebra Appl. 429, No. 1, 110--121 (2008; Zbl 1148.15012) Full Text: DOI
Liao, Anping The positive definite solution of the matrix equation \(X+A^*X^{-n}A=I\). (Chinese. English summary) Zbl 1065.15017 Numer. Math., Nanjing 26, No. 2, 156-161 (2004). MSC: 15A24 65F30 65F10 PDFBibTeX XMLCite \textit{A. Liao}, Numer. Math., Nanjing 26, No. 2, 156--161 (2004; Zbl 1065.15017)
Liao, Anping; Zhang, Lei The necessary and sufficient conditions for the solvability of a class of the matrix inverse problem. (English) Zbl 0935.15016 Numer. Math., J. Chin. Univ. 7, No. 2, 195-200 (1998). MSC: 15A24 PDFBibTeX XMLCite \textit{A. Liao} and \textit{L. Zhang}, Numer. Math., J. Chin. Univ. 7, No. 2, 195--200 (1998; Zbl 0935.15016)
Liao, Anping A class of inverse problems of matrices and its best approximation on the linear manifold. (English) Zbl 0904.15004 Acta Sci. Nat. Univ. Norm. Hunanensis 21, No. 1, 4-9 (1998). Reviewer: M.Voicu (Iaşi) MSC: 15A09 15A24 PDFBibTeX XMLCite \textit{A. Liao}, Acta Sci. Nat. Univ. Norm. Hunanensis 21, No. 1, 4--9 (1998; Zbl 0904.15004)
Liao, Anping Symmetric positive semidefinite solutions of the matrix equation \((A^TXA,B^TXB)=(C,D)\). (Chinese. English summary) Zbl 0905.15005 Acta Sci. Nat. Univ. Norm. Hunanensis 20, No. 4, 10-13, 29 (1997). Reviewer: Chen Zhijie (Shanghai) MSC: 15A24 PDFBibTeX XMLCite \textit{A. Liao}, Acta Sci. Nat. Univ. Norm. Hunanensis 20, No. 4, 10--13, 29 (1997; Zbl 0905.15005)