Sadek, Lakhlifa; Talibi Alaoui, Hamad Numerical methods for solving large-scale systems of differential equations. (English) Zbl 1526.65014 Ric. Mat. 72, No. 2, 785-802 (2023). MSC: 65F50 15A24 65F10 65L05 PDFBibTeX XMLCite \textit{L. Sadek} and \textit{H. Talibi Alaoui}, Ric. Mat. 72, No. 2, 785--802 (2023; Zbl 1526.65014) Full Text: DOI
Cheraghzadeh, T.; Toutounian, F.; Ghaziani, R. Khoshsiar Global and extended global Hessenberg processes for solving Sylvester tensor equation with low-rank right-hand side. (English) Zbl 1499.65142 Iran. J. Numer. Anal. Optim. 12, No. 3, 658-679 (2022). MSC: 65F45 15A69 15A24 PDFBibTeX XMLCite \textit{T. Cheraghzadeh} et al., Iran. J. Numer. Anal. Optim. 12, No. 3, 658--679 (2022; Zbl 1499.65142) Full Text: DOI
Cheraghzadeh, T.; Ghaziani, R. Khoshsiar; Toutounian, F. Projection schemes based on Hessenberg process for Sylvester tensor equation with low-rank right-hand side. (English) Zbl 1513.65116 Comput. Appl. Math. 41, No. 7, Paper No. 311, 18 p. (2022). MSC: 65F45 15A24 15A69 PDFBibTeX XMLCite \textit{T. Cheraghzadeh} et al., Comput. Appl. Math. 41, No. 7, Paper No. 311, 18 p. (2022; Zbl 1513.65116) Full Text: DOI
Bentbib, Abdeslem Hafid; El-Halouy, Smahane; Sadek, El Mostafa Extended Krylov subspace methods for solving Sylvester and Stein tensor equations. (English) Zbl 1500.15019 Discrete Contin. Dyn. Syst., Ser. S 15, No. 1, 41-56 (2022). MSC: 15A69 15A24 47A62 65F99 PDFBibTeX XMLCite \textit{A. H. Bentbib} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 1, 41--56 (2022; Zbl 1500.15019) Full Text: DOI
Huang, Guang-Xin; Chen, Qi-Xing; Yin, Feng Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation. (English) Zbl 1510.65080 Appl. Math. Comput. 422, Article ID 126984, 14 p. (2022). MSC: 65F45 15A24 15A69 65F08 PDFBibTeX XMLCite \textit{G.-X. Huang} et al., Appl. Math. Comput. 422, Article ID 126984, 14 p. (2022; Zbl 1510.65080) Full Text: DOI arXiv
Saberi-Movahed, Farid; Tajaddini, Azita; Heyouni, Mohammed; Elbouyahyaoui, Lakhdar Some iterative approaches for Sylvester tensor equations. II: A tensor format of simpler variant of GCRO-based methods. (English) Zbl 1484.65078 Appl. Numer. Math. 172, 413-427 (2022). MSC: 65F45 15A69 PDFBibTeX XMLCite \textit{F. Saberi-Movahed} et al., Appl. Numer. Math. 172, 413--427 (2022; Zbl 1484.65078) Full Text: DOI
Sadek, Lakhlifa; Talibi, Alaoui Hamad The extended block Arnoldi method for solving generalized differential Sylvester equations. (English) Zbl 1474.65113 J. Math. Model. 8, No. 2, 189-206 (2020). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{L. Sadek} and \textit{A. H. Talibi}, J. Math. Model. 8, No. 2, 189--206 (2020; Zbl 1474.65113) Full Text: DOI
Bentbib, A. H.; El-Halouy, S.; Sadek, El M. Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side. (English) Zbl 1450.65039 Numer. Algorithms 84, No. 4, 1411-1430 (2020). Reviewer: Ctirad Matonoha (Praha) MSC: 65F45 15A69 15A24 PDFBibTeX XMLCite \textit{A. H. Bentbib} et al., Numer. Algorithms 84, No. 4, 1411--1430 (2020; Zbl 1450.65039) Full Text: DOI
Kaouane, Y. A tangential method for the balanced truncation in model reduction. (English) Zbl 1433.65077 Numer. Algorithms 83, No. 2, 629-652 (2020). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{Y. Kaouane}, Numer. Algorithms 83, No. 2, 629--652 (2020; Zbl 1433.65077) Full Text: DOI
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. (English) Zbl 1385.65035 Numer. Math. 138, No. 2, 301-330 (2018). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Math. 138, No. 2, 301--330 (2018; Zbl 1385.65035) Full Text: DOI arXiv
Simoncini, V. Computational methods for linear matrix equations. (English) Zbl 1386.65124 SIAM Rev. 58, No. 3, 377-441 (2016). MSC: 65F30 65F10 15A24 15A06 PDFBibTeX XMLCite \textit{V. Simoncini}, SIAM Rev. 58, No. 3, 377--441 (2016; Zbl 1386.65124) Full Text: DOI Link
Massoudi, Arash; Opmeer, Mark R.; Reis, Timo Analysis of an iteration method for the algebraic Riccati equation. (English) Zbl 1339.15010 SIAM J. Matrix Anal. Appl. 37, No. 2, 624-648 (2016). MSC: 15A24 49N10 47J20 65F30 49M30 93B52 65K10 PDFBibTeX XMLCite \textit{A. Massoudi} et al., SIAM J. Matrix Anal. Appl. 37, No. 2, 624--648 (2016; Zbl 1339.15010) Full Text: DOI Link
Bouhamidi, A.; Hached, M.; Jbilou, K. A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations. (English) Zbl 1339.49024 J. Glob. Optim. 65, No. 1, 19-32 (2016). MSC: 49M15 65F30 15A24 PDFBibTeX XMLCite \textit{A. Bouhamidi} et al., J. Glob. Optim. 65, No. 1, 19--32 (2016; Zbl 1339.49024) Full Text: DOI
Lin, Yiding; Simoncini, Valeria A new subspace iteration method for the algebraic Riccati equation. (English) Zbl 1363.65076 Numer. Linear Algebra Appl. 22, No. 1, 26-47 (2015). MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{Y. Lin} and \textit{V. Simoncini}, Numer. Linear Algebra Appl. 22, No. 1, 26--47 (2015; Zbl 1363.65076) Full Text: DOI arXiv
Lang, Norman; Mena, Hermann; Saak, Jens On the benefits of the \(L D L^T\) factorization for large-scale differential matrix equation solvers. (English) Zbl 1320.65110 Linear Algebra Appl. 480, 44-71 (2015). MSC: 65L06 15A23 93A15 PDFBibTeX XMLCite \textit{N. Lang} et al., Linear Algebra Appl. 480, 44--71 (2015; Zbl 1320.65110) Full Text: DOI
Kressner, Daniel; Plešinger, Martin; Tobler, Christine A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations. (English) Zbl 1340.65077 Numer. Linear Algebra Appl. 21, No. 5, 666-684 (2014). Reviewer: Ninoslav Truhar (Osijek) MSC: 65F30 15A24 65F08 65F10 PDFBibTeX XMLCite \textit{D. Kressner} et al., Numer. Linear Algebra Appl. 21, No. 5, 666--684 (2014; Zbl 1340.65077) Full Text: DOI
Simoncini, Valeria; Szyld, Daniel B.; Monsalve, Marlliny On two numerical methods for the solution of large-scale algebraic Riccati equations. (English) Zbl 1298.65083 IMA J. Numer. Anal. 34, No. 3, 904-920 (2014). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{V. Simoncini} et al., IMA J. Numer. Anal. 34, No. 3, 904--920 (2014; Zbl 1298.65083) Full Text: DOI
Bouhamidi, Abderrahman; Hached, M.; Heyouni, M.; Jbilou, Khalide A preconditioned block Arnoldi method for large Sylvester matrix equations. (English) Zbl 1289.65099 Numer. Linear Algebra Appl. 20, No. 2, 208-219 (2013). Reviewer: Ninoslav Truhar (Osijek) MSC: 65F30 65F08 65F10 15A24 PDFBibTeX XMLCite \textit{A. Bouhamidi} et al., Numer. Linear Algebra Appl. 20, No. 2, 208--219 (2013; Zbl 1289.65099) Full Text: DOI
Benner, Peter; Saak, Jens Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey. (English) Zbl 1279.65044 GAMM-Mitt. 36, No. 1, 32-52 (2013). MSC: 65F30 15A24 65F10 65-02 PDFBibTeX XMLCite \textit{P. Benner} and \textit{J. Saak}, GAMM-Mitt. 36, No. 1, 32--52 (2013; Zbl 1279.65044) Full Text: DOI
Benner, Peter; Kürschner, Patrick; Saak, Jens Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method. (English) Zbl 1267.65047 Numer. Algorithms 62, No. 2, 225-251 (2013). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65F30 65F10 15A24 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algorithms 62, No. 2, 225--251 (2013; Zbl 1267.65047) Full Text: DOI
Bini, Dario A.; Iannazzo, Bruno; Meini, Beatrice Numerical solution of algebraic Riccati equations. (English) Zbl 1244.65058 Fundamentals of Algorithms 9. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611972-08-5/pbk; 978-1-611972-09-2/ebook). xvi, 250 p. (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 15A24 65-02 PDFBibTeX XMLCite \textit{D. A. Bini} et al., Numerical solution of algebraic Riccati equations. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2012; Zbl 1244.65058) Full Text: DOI Link
Druskin, Vladimir; Knizhnerman, Leonid; Simoncini, Valeria Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation. (English) Zbl 1244.65060 SIAM J. Numer. Anal. 49, No. 5, 1875-1898 (2011). Reviewer: Frank Uhlig (Auburn) MSC: 65F30 65F10 15A24 93B40 PDFBibTeX XMLCite \textit{V. Druskin} et al., SIAM J. Numer. Anal. 49, No. 5, 1875--1898 (2011; Zbl 1244.65060) Full Text: DOI Link
Benner, Peter; Faßbender, Heike On the numerical solution of large-scale sparse discrete-time Riccati equations. (English) Zbl 1230.65070 Adv. Comput. Math. 35, No. 2-4, 119-147 (2011). MSC: 65K10 49J20 49M15 49N10 65F30 15A24 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Faßbender}, Adv. Comput. Math. 35, No. 2--4, 119--147 (2011; Zbl 1230.65070) Full Text: DOI
Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. (English) Zbl 1193.65045 Syst. Control Lett. 59, No. 3-4, 248-257 (2010). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{N. Truhar} et al., Syst. Control Lett. 59, No. 3--4, 248--257 (2010; Zbl 1193.65045) Full Text: DOI
Jbilou, K. ADI preconditioned Krylov methods for large Lyapunov matrix equations. (English) Zbl 1189.65078 Linear Algebra Appl. 432, No. 10, 2473-2485 (2010). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{K. Jbilou}, Linear Algebra Appl. 432, No. 10, 2473--2485 (2010; Zbl 1189.65078) Full Text: DOI
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav On the ADI method for Sylvester equations. (English) Zbl 1176.65050 J. Comput. Appl. Math. 233, No. 4, 1035-1045 (2009). MSC: 65F30 15A24 40C05 37L99 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Appl. Math. 233, No. 4, 1035--1045 (2009; Zbl 1176.65050) Full Text: DOI
Kressner, Daniel; Schröder, Christian; Watkins, David S. Implicit QR algorithms for palindromic and even eigenvalue problems. (English) Zbl 1181.65054 Numer. Algorithms 51, No. 2, 209-238 (2009). Reviewer: J. B. Butler jun. (Portland) MSC: 65F15 15A21 PDFBibTeX XMLCite \textit{D. Kressner} et al., Numer. Algorithms 51, No. 2, 209--238 (2009; Zbl 1181.65054) Full Text: DOI Link
Saak, Jens; Benner, Peter Efficient solution of large scale Lyapunov and Riccati equations arising in model order reduction problems. (English) Zbl 1392.65109 PAMM, Proc. Appl. Math. Mech. 8, 10085-10088 (2008). MSC: 65K10 65F30 15A24 93C05 65F50 65H10 49N10 49N35 93B52 PDFBibTeX XMLCite \textit{J. Saak} and \textit{P. Benner}, PAMM, Proc. Appl. Math. Mech. 8, 10085--10088 (2008; Zbl 1392.65109) Full Text: DOI
Benner, Peter; Li, Jing-Rebecca; Penzl, Thilo Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. (English) Zbl 1212.65245 Numer. Linear Algebra Appl. 15, No. 9, 755-777 (2008). MSC: 65K10 65F30 15A24 93C05 65F50 65H10 49N10 49N35 93B52 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Linear Algebra Appl. 15, No. 9, 755--777 (2008; Zbl 1212.65245) Full Text: DOI
Heyouni, M.; Jbilou, K.; Messaoudi, A.; Tabaa, K. Model reduction in large scale MIMO dynamical systems via the block Lanczos method. (English) Zbl 1167.65021 Comput. Appl. Math. 27, No. 2, 211-236 (2008). Reviewer: Vasilis Dimitriou (Chania) MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{M. Heyouni} et al., Comput. Appl. Math. 27, No. 2, 211--236 (2008; Zbl 1167.65021)
Simoncini, V. A new iterative method for solving large-scale Lyapunov matrix equations. (English) Zbl 1146.65038 SIAM J. Sci. Comput. 29, No. 3, 1268-1288 (2007). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{V. Simoncini}, SIAM J. Sci. Comput. 29, No. 3, 1268--1288 (2007; Zbl 1146.65038) Full Text: DOI
Truhar, Ninoslav; Veselić, KreŠimir Bounds on the trace of a solution to the Lyapunov equation with a general stable matrix. (English) Zbl 1117.93066 Syst. Control Lett. 56, No. 7-8, 493-503 (2007). MSC: 93D30 93B60 15A24 15A18 PDFBibTeX XMLCite \textit{N. Truhar} and \textit{K. Veselić}, Syst. Control Lett. 56, No. 7--8, 493--503 (2007; Zbl 1117.93066) Full Text: DOI
Benner, Peter Numerical linear algebra for model reduction in control and simulation. (English) Zbl 1157.93337 GAMM-Mitt. 29, No. 2, 275-296 (2006). MSC: 93B11 65F30 41A20 65F15 93-02 15A18 PDFBibTeX XMLCite \textit{P. Benner}, GAMM-Mitt. 29, No. 2, 275--296 (2006; Zbl 1157.93337) Full Text: DOI
Heyouni, M.; Jbilou, K. Matrix Krylov subspace methods for large scale model reduction problems. (English) Zbl 1115.65042 Appl. Math. Comput. 181, No. 2, 1215-1228 (2006). Reviewer: Keehwan Kim (Kyongsan) MSC: 65F30 15A24 93C05 PDFBibTeX XMLCite \textit{M. Heyouni} and \textit{K. Jbilou}, Appl. Math. Comput. 181, No. 2, 1215--1228 (2006; Zbl 1115.65042) Full Text: DOI
Penzl, Thilo Numerical solution of generalized Lyapunov equations. (English) Zbl 0909.65026 Adv. Comput. Math. 8, No. 1-2, 33-48 (1998). Reviewer: P.Narain (Bombay) MSC: 65F30 65K10 15A24 93C55 PDFBibTeX XMLCite \textit{T. Penzl}, Adv. Comput. Math. 8, No. 1--2, 33--48 (1998; Zbl 0909.65026) Full Text: DOI