Chen, Xiao Shan; Xu, Hongguo QR algorithm with two-sided Rayleigh quotient shifts. (English) Zbl 07790613 Numer. Linear Algebra Appl. 30, No. 5, e2487, 31 p. (2023). MSC: 65F15 PDFBibTeX XMLCite \textit{X. S. Chen} and \textit{H. Xu}, Numer. Linear Algebra Appl. 30, No. 5, e2487, 31 p. (2023; Zbl 07790613) Full Text: DOI
Chen, Xiao Shan; Xu, Hongguo QZ algorithm with two-sided generalized Rayleigh quotient shifts. (English) Zbl 07729592 Numer. Linear Algebra Appl. 30, No. 4, e2475, 27 p. (2023). MSC: 65F15 PDFBibTeX XMLCite \textit{X. S. Chen} and \textit{H. Xu}, Numer. Linear Algebra Appl. 30, No. 4, e2475, 27 p. (2023; Zbl 07729592) Full Text: DOI
Mehrmann, Volker; Xu, Hongguo Eigenstructure perturbations for a class of Hamiltonian matrices and solutions of related Riccati inequalities. arXiv:2311.14202 Preprint, arXiv:2311.14202 [math.OC] (2023). MSC: 65F15 65H10 93D15 BibTeX Cite \textit{V. Mehrmann} and \textit{H. Xu}, ``Eigenstructure perturbations for a class of Hamiltonian matrices and solutions of related Riccati inequalities'', Preprint, arXiv:2311.14202 [math.OC] (2023) Full Text: arXiv OA License
Xu, Hongguo Invariant subspace perturbation of a matrix with Jordan blocks. arXiv:2311.12219 Preprint, arXiv:2311.12219 [math.NA] (2023). MSC: 15A18 47A55 65F15 BibTeX Cite \textit{H. Xu}, ``Invariant subspace perturbation of a matrix with Jordan blocks'', Preprint, arXiv:2311.12219 [math.NA] (2023) Full Text: arXiv OA License
Chen, Xiao Shan; Xu, Hongguo Two-sided Rayleigh quotient iteration for periodic eigenvalue problems. (English) Zbl 07511603 Numer. Linear Algebra Appl. 29, No. 3, e2422, 21 p. (2022). MSC: 65F15 PDFBibTeX XMLCite \textit{X. S. Chen} and \textit{H. Xu}, Numer. Linear Algebra Appl. 29, No. 3, e2422, 21 p. (2022; Zbl 07511603) Full Text: DOI
Xu, Hongguo A core-chasing symplectic QR algorithm. (English) Zbl 1461.65050 SIAM J. Matrix Anal. Appl. 41, No. 2, 901-927 (2020). MSC: 65F15 65H10 PDFBibTeX XMLCite \textit{H. Xu}, SIAM J. Matrix Anal. Appl. 41, No. 2, 901--927 (2020; Zbl 1461.65050) Full Text: DOI
Chen, Xiao Shan; Vong, Seak-Weng; Li, Wen; Xu, Hongguo Noda iterations for generalized eigenproblems following Perron-Frobenius theory. (English) Zbl 07037512 Numer. Algorithms 80, No. 3, 937-955 (2019). Reviewer: Edgar Pereira (Natal) MSC: 65F15 PDFBibTeX XMLCite \textit{X. S. Chen} et al., Numer. Algorithms 80, No. 3, 937--955 (2019; Zbl 07037512) Full Text: DOI
Beattie, Christopher; Mehrmann, Volker; Xu, Hongguo; Zwart, Hans Linear port-Hamiltonian descriptor systems. (English) Zbl 1401.37070 Math. Control Signals Syst. 30, No. 4, Paper No. 17, 27 p. (2018). MSC: 37K05 65L80 93B17 93B11 93C15 93C05 PDFBibTeX XMLCite \textit{C. Beattie} et al., Math. Control Signals Syst. 30, No. 4, Paper No. 17, 27 p. (2018; Zbl 1401.37070) Full Text: DOI arXiv Link
Calvetti, D.; Reichel, L.; Xu, H. A CS decomposition for orthogonal matrices with application to eigenvalue computation. (English) Zbl 1316.65044 Linear Algebra Appl. 476, 197-232 (2015). MSC: 65F15 15A23 15B10 PDFBibTeX XMLCite \textit{D. Calvetti} et al., Linear Algebra Appl. 476, 197--232 (2015; Zbl 1316.65044) Full Text: DOI
Mehrmann, Volker; Xu, Hongguo Structure preserving deflation of infinite eigenvalues in structured pencils. (English) Zbl 1312.65055 ETNA, Electron. Trans. Numer. Anal. 44, 1-24 (2015). MSC: 65F15 15A21 15A22 93B36 93B60 65K10 PDFBibTeX XMLCite \textit{V. Mehrmann} and \textit{H. Xu}, ETNA, Electron. Trans. Numer. Anal. 44, 1--24 (2015; Zbl 1312.65055) Full Text: EMIS
Kamenski, Lennard; Huang, Weizhang; Xu, Hongguo Conditioning of finite element equations with arbitrary anisotropic meshes. (English) Zbl 1303.65097 Math. Comput. 83, No. 289, 2187-2211 (2014). Reviewer: Ivan Secrieru (Chişinău) MSC: 65N30 65F35 35J25 65N50 PDFBibTeX XMLCite \textit{L. Kamenski} et al., Math. Comput. 83, No. 289, 2187--2211 (2014; Zbl 1303.65097) Full Text: DOI arXiv
Xu, Hongguo Functions of a matrix and Krylov matrices. (English) Zbl 1390.15069 Linear Algebra Appl. 434, No. 1, 185-200 (2011). MSC: 15A54 15A21 65F15 15A16 PDFBibTeX XMLCite \textit{H. Xu}, Linear Algebra Appl. 434, No. 1, 185--200 (2011; Zbl 1390.15069) Full Text: DOI
Mehl, Christian; Mehrmann, Volker; Xu, Hongguo Singular-value-like decomposition for complex matrix triples. (English) Zbl 1186.65048 J. Comput. Appl. Math. 233, No. 5, 1245-1276 (2010). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F20 65F15 15A21 15B57 PDFBibTeX XMLCite \textit{C. Mehl} et al., J. Comput. Appl. Math. 233, No. 5, 1245--1276 (2010; Zbl 1186.65048) Full Text: DOI
Mehl, Christian; Mehrmann, Volker; Xu, Hongguo Structured decompositions for matrix triples: SVD-like concepts for structured matrices. (English) Zbl 1188.15012 Oper. Matrices 3, No. 3, Article ID 19, 303-356 (2009). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 15A21 65F15 65L80 PDFBibTeX XMLCite \textit{C. Mehl} et al., Oper. Matrices 3, No. 3, Article ID 19, 303--356 (2009; Zbl 1188.15012) Full Text: Link
Mehrmann, Volker; Xu, Hongguo Explicit solutions for a Riccati equation from transport theory. (English) Zbl 1176.65055 SIAM J. Matrix Anal. Appl. 30, No. 4, 1339-1357 (2008). MSC: 65F30 15A24 15A18 82C70 PDFBibTeX XMLCite \textit{V. Mehrmann} and \textit{H. Xu}, SIAM J. Matrix Anal. Appl. 30, No. 4, 1339--1357 (2008; Zbl 1176.65055) Full Text: DOI Link
Byers, Ralph; Xu, Hongguo A new scaling for Newton’s iteration for the polar decomposition and its backward stability. (English) Zbl 1170.65019 SIAM J. Matrix Anal. Appl. 30, No. 2, 822-843 (2008). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65F05 PDFBibTeX XMLCite \textit{R. Byers} and \textit{H. Xu}, SIAM J. Matrix Anal. Appl. 30, No. 2, 822--843 (2008; Zbl 1170.65019) Full Text: DOI Link
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo Trimmed linearizations for structured matrix polynomials. (English) Zbl 1155.65026 Linear Algebra Appl. 429, No. 10, 2373-2400 (2008). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F15 15A21 15A54 PDFBibTeX XMLCite \textit{R. Byers} et al., Linear Algebra Appl. 429, No. 10, 2373--2400 (2008; Zbl 1155.65026) Full Text: DOI
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo A robust numerical method for the \(\gamma\)-iteration in \(H_{\infty}\) control. (English) Zbl 1124.93022 Linear Algebra Appl. 425, No. 2-3, 548-570 (2007). MSC: 93B40 93B36 65F15 93B52 93C05 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 425, No. 2--3, 548--570 (2007; Zbl 1124.93022) Full Text: DOI
Xu, Hongguo Transformations between discrete-time and continuous-time algebraic Riccati equations. (English) Zbl 1135.93009 Linear Algebra Appl. 425, No. 1, 77-101 (2007). MSC: 93B17 93B40 93B36 15A18 15A22 65F15 93B60 93B05 PDFBibTeX XMLCite \textit{H. Xu}, Linear Algebra Appl. 425, No. 1, 77--101 (2007; Zbl 1135.93009) Full Text: DOI
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo A structured staircase algorithm for skew-symmetric/symmetric pencils. (English) Zbl 1113.65065 ETNA, Electron. Trans. Numer. Anal. 26, 1-33 (2007). Reviewer: Thomas Sonar (Braunschweig) MSC: 65K10 65F15 15A21 93B40 49N10 PDFBibTeX XMLCite \textit{R. Byers} et al., ETNA, Electron. Trans. Numer. Anal. 26, 1--33 (2007; Zbl 1113.65065) Full Text: EuDML Link
Xu, Hongguo A numerical method for computing an SVD-like decomposition. (English) Zbl 1114.65036 SIAM J. Matrix Anal. Appl. 26, No. 4, 1058-1082 (2005). MSC: 65F15 PDFBibTeX XMLCite \textit{H. Xu}, SIAM J. Matrix Anal. Appl. 26, No. 4, 1058--1082 (2005; Zbl 1114.65036) Full Text: DOI
Mehl, Christian; Mehrmann, Volker; Xu, Hongguo On doubly structured matrices and pencils that arise in linear response theory. (English) Zbl 1083.65038 Linear Algebra Appl. 380, 3-51 (2004). Reviewer: Bui Doan Khanh (Paris) MSC: 65F15 15A21 15A22 15B57 93B25 PDFBibTeX XMLCite \textit{C. Mehl} et al., Linear Algebra Appl. 380, 3--51 (2004; Zbl 1083.65038) Full Text: DOI
Xu, Hongguo An SVD-like matrix decomposition and its applications. (English) Zbl 1025.15016 Linear Algebra Appl. 368, 1-24 (2003). Reviewer: Erich Ellers (Toronto) MSC: 15A23 15B57 15A18 65F20 15A21 PDFBibTeX XMLCite \textit{H. Xu}, Linear Algebra Appl. 368, 1--24 (2003; Zbl 1025.15016) Full Text: DOI
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. (English) Zbl 1035.49022 SIAM J. Matrix Anal. Appl. 24, No. 1, 165-190 (2002). MSC: 49N10 65F15 93B40 93B36 15A22 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Matrix Anal. Appl. 24, No. 1, 165--190 (2002; Zbl 1035.49022) Full Text: DOI
Benner, Peter; Mehrmann, Volker; Xu, Hongguo Perturbation analysis for the eigenvalue problem of a formal product of matrices. (English) Zbl 1003.65032 BIT 42, No. 1, 1-43 (2002). Reviewer: Horst Hollatz (Magdeburg) MSC: 65F15 15A42 PDFBibTeX XMLCite \textit{P. Benner} et al., BIT 42, No. 1, 1--43 (2002; Zbl 1003.65032) Full Text: DOI
Freiling, Gerhard; Mehrmann, Volker; Xu, Hongguo Existence, uniqueness, and parametrization of Lagrangian invariant subspaces. (English) Zbl 1029.65044 SIAM J. Matrix Anal. Appl. 23, No. 4, 1045-1069 (2002). Reviewer: E.Kreyszig (Ottawa) MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{G. Freiling} et al., SIAM J. Matrix Anal. Appl. 23, No. 4, 1045--1069 (2002; Zbl 1029.65044) Full Text: DOI
Mehrmann, Volker; Xu, Hongguo Numerical methods in control. (English) Zbl 0967.65081 J. Comput. Appl. Math. 123, No. 1-2, 371-394 (2000). Reviewer: J.Vaníček (Praha) MSC: 65K10 93D15 93B40 93B36 PDFBibTeX XMLCite \textit{V. Mehrmann} and \textit{H. Xu}, J. Comput. Appl. Math. 123, No. 1--2, 371--394 (2000; Zbl 0967.65081) Full Text: DOI
Benner, Peter; Mehrmann, Volker; Xu, Hongguo A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems. (English) Zbl 0936.65045 ETNA, Electron. Trans. Numer. Anal. 8, 115-126 (1999). Reviewer: J.B.Butler jun.(Portland) MSC: 65F15 93B36 93B40 PDFBibTeX XMLCite \textit{P. Benner} et al., ETNA, Electron. Trans. Numer. Anal. 8, 115--126 (1999; Zbl 0936.65045) Full Text: EuDML EMIS
Mehrmann, Volker; Xu, Hongguo Choosing poles so that the single-input pole placement problem is well conditioned. (English) Zbl 0919.93031 SIAM J. Matrix Anal. Appl. 19, No. 3, 664-681 (1998). Reviewer: Petko Hr.Petkov (Sofia) MSC: 93B55 65F15 93B60 65F35 65G50 93B05 PDFBibTeX XMLCite \textit{V. Mehrmann} and \textit{H. Xu}, SIAM J. Matrix Anal. Appl. 19, No. 3, 664--681 (1998; Zbl 0919.93031) Full Text: DOI
Xu, Hongguo The relation between the QR and LR algorithms. (English) Zbl 0916.65033 SIAM J. Matrix Anal. Appl. 19, No. 2, 551-555 (1998). Reviewer: Lubomír Bakule (Praha) MSC: 65F15 PDFBibTeX XMLCite \textit{H. Xu}, SIAM J. Matrix Anal. Appl. 19, No. 2, 551--555 (1998; Zbl 0916.65033) Full Text: DOI
Benner, Peter; Mehrmann, Volker; Xu, Hongguo A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils. (English) Zbl 0889.65036 Numer. Math. 78, No. 3, 329-358 (1998). Reviewer: G.Jumarie (Montréal) MSC: 65F15 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Math. 78, No. 3, 329--358 (1998; Zbl 0889.65036) Full Text: DOI Link
Mehrmann, Volker; Xu, Hongguo An analysis of the pole placement problem. II: The multi-input case. (English) Zbl 0899.93017 ETNA, Electron. Trans. Numer. Anal. 5, 77-97 (1997). Reviewer: Petko Hr.Petkov (Sofia) MSC: 93B55 93C35 65F15 65F35 65G50 93B05 PDFBibTeX XMLCite \textit{V. Mehrmann} and \textit{H. Xu}, ETNA, Electron. Trans. Numer. Anal. 5, 77--97 (1997; Zbl 0899.93017) Full Text: EuDML EMIS
Benner, Peter; Mehrmann, Volker; Xu, Hongguo A new method for computing the stable invariant subspace of a real Hamiltonian matrix. (English) Zbl 1005.65034 J. Comput. Appl. Math. 86, No. 1, 17-43 (1997). Reviewer: J.P.Milaszewicz (Dublin) MSC: 65F15 15B57 15A24 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Appl. Math. 86, No. 1, 17--43 (1997; Zbl 1005.65034) Full Text: DOI
Mehrmann, Volker; Xu, Hongguo An analysis of the pole placement problem I: The single-input case. (English) Zbl 0890.65036 ETNA, Electron. Trans. Numer. Anal. 4, 89-105 (1996). Reviewer: A.Meister (Hamburg) MSC: 65F15 65F35 93B55 PDFBibTeX XMLCite \textit{V. Mehrmann} and \textit{H. Xu}, ETNA, Electron. Trans. Numer. Anal. 4, 89--105 (1996; Zbl 0890.65036) Full Text: EuDML EMIS
Xu, Hongguo; Lu, Linzhang Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation. (English) Zbl 0832.65042 Linear Algebra Appl. 222, 127-145 (1995). Reviewer: V.Prepeliţă (Bucureşti) MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{H. Xu} and \textit{L. Lu}, Linear Algebra Appl. 222, 127--145 (1995; Zbl 0832.65042) Full Text: DOI