Scarciotti, Giordano; Astolfi, Alessandro Interconnection-based model order reduction – a survey. (English) Zbl 07803802 Eur. J. Control 75, Article ID 100929, 17 p. (2024). MSC: 93B11 93B70 93C10 93C30 93E03 93-02 PDFBibTeX XMLCite \textit{G. Scarciotti} and \textit{A. Astolfi}, Eur. J. Control 75, Article ID 100929, 17 p. (2024; Zbl 07803802) Full Text: DOI
Edelman, Alan; Jeong, Sungwoo Fifty three matrix factorizations: a systematic approach. (English) Zbl 1518.15018 SIAM J. Matrix Anal. Appl. 44, No. 2, 415-480 (2023). MSC: 15A23 22E60 15A30 22E70 PDFBibTeX XMLCite \textit{A. Edelman} and \textit{S. Jeong}, SIAM J. Matrix Anal. Appl. 44, No. 2, 415--480 (2023; Zbl 1518.15018) Full Text: DOI arXiv
Sakamoto, Hiroki; Sato, Kazuhiro Random projection preserves stability with high probability. (English) Zbl 1526.65015 JSIAM Lett. 15, 17-20 (2023). MSC: 65F55 65F15 65P99 65L99 PDFBibTeX XMLCite \textit{H. Sakamoto} and \textit{K. Sato}, JSIAM Lett. 15, 17--20 (2023; Zbl 1526.65015) Full Text: DOI
Edelman, Alan; Jeong, Sungwoo On the Cartan decomposition for classical random matrix ensembles. (English) Zbl 1508.15026 J. Math. Phys. 63, No. 6, Article ID 061705, 24 p. (2022). MSC: 15B52 15A21 53C35 PDFBibTeX XMLCite \textit{A. Edelman} and \textit{S. Jeong}, J. Math. Phys. 63, No. 6, Article ID 061705, 24 p. (2022; Zbl 1508.15026) Full Text: DOI arXiv
Hamadi, M. A.; Jbilou, K.; Ratnani, A. A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method. (English) Zbl 1487.65042 J. Appl. Math. Comput. 68, No. 1, 271-293 (2022). MSC: 65F15 65F50 65P99 93B11 PDFBibTeX XMLCite \textit{M. A. Hamadi} et al., J. Appl. Math. Comput. 68, No. 1, 271--293 (2022; Zbl 1487.65042) Full Text: DOI
Motlaghian, Sara M.; Armandnejad, Ali; Hall, Frank J. A note on some classes of G-matrices. (English) Zbl 1490.15041 Oper. Matrices 16, No. 1, 251-263 (2022). MSC: 15B10 15A20 15A30 PDFBibTeX XMLCite \textit{S. M. Motlaghian} et al., Oper. Matrices 16, No. 1, 251--263 (2022; Zbl 1490.15041) Full Text: DOI
Chkifa, A.; Hamadi, M. A.; Jbilou, K.; Ratnani, A. A computational method for model reduction in index-2 dynamical systems for Stokes equations. (English) Zbl 1524.65521 Comput. Math. Appl. 99, 171-181 (2021). MSC: 65M60 65L80 76D07 PDFBibTeX XMLCite \textit{A. Chkifa} et al., Comput. Math. Appl. 99, 171--181 (2021; Zbl 1524.65521) Full Text: DOI
Nouri, Behzad; Gad, Emad; Nakhla, Michel; Achar, Ram Model order reduction in microelectronics. (English) Zbl 1466.78016 Benner, Peter (ed.) et al., Model order reduction. Volume 3: Applications. Berlin: De Gruyter. 111-143 (2021). MSC: 78A55 62P30 93A15 78M34 37M05 34K20 34H15 94C05 PDFBibTeX XMLCite \textit{B. Nouri} et al., in: Model order reduction. Volume 3: Applications. Berlin: De Gruyter. 111--143 (2021; Zbl 1466.78016) Full Text: DOI
Embree, Mark Unstable modes in projection-based reduced-order models: how many can there be, and what do they tell you? (English) Zbl 1408.93034 Syst. Control Lett. 124, 49-59 (2019). MSC: 93B11 93A15 93C05 93B60 93C55 PDFBibTeX XMLCite \textit{M. Embree}, Syst. Control Lett. 124, 49--59 (2019; Zbl 1408.93034) Full Text: DOI arXiv
Fung, Samy Wu; Ruthotto, Lars A multiscale method for model order reduction in PDE parameter estimation. (English) Zbl 1524.76241 J. Comput. Appl. Math. 350, 19-34 (2019). MSC: 76M12 76S05 65K10 65N30 35R30 PDFBibTeX XMLCite \textit{S. W. Fung} and \textit{L. Ruthotto}, J. Comput. Appl. Math. 350, 19--34 (2019; Zbl 1524.76241) Full Text: DOI arXiv
Motlaghian, Sara M.; Armandnejad, Ali; Hall, Frank J. Topological properties of \(J\)-orthogonal matrices. (English) Zbl 1430.15023 Linear Multilinear Algebra 66, No. 12, 2524-2533 (2018). Reviewer: Julio Benítez (Valencia) MSC: 15B10 15A30 PDFBibTeX XMLCite \textit{S. M. Motlaghian} et al., Linear Multilinear Algebra 66, No. 12, 2524--2533 (2018; Zbl 1430.15023) Full Text: DOI
Hall, Frank J.; Li, Zhongshan; Parnass, Caroline T.; Rozložník, Miroslav Sign patterns of \(J\)-orthogonal matrices. (English) Zbl 1392.15045 Spec. Matrices 5, 225-241 (2017). MSC: 15B35 15B10 PDFBibTeX XMLCite \textit{F. J. Hall} et al., Spec. Matrices 5, 225--241 (2017; Zbl 1392.15045) Full Text: DOI
Mohamed, K.; Mehdi, A.; Abdelkader, M. An iterative model order reduction method for large-scale dynamical systems. (English) Zbl 1373.93073 ANZIAM J. 59, No. 1, 115-133 (2017). MSC: 93B11 93A15 93C05 65F15 PDFBibTeX XMLCite \textit{K. Mohamed} et al., ANZIAM J. 59, No. 1, 115--133 (2017; Zbl 1373.93073) Full Text: DOI
Abidi, O.; Hached, M.; Jbilou, K. A global rational Arnoldi method for model reduction. (English) Zbl 1365.65079 J. Comput. Appl. Math. 325, 175-187 (2017). MSC: 65F10 65F30 PDFBibTeX XMLCite \textit{O. Abidi} et al., J. Comput. Appl. Math. 325, 175--187 (2017; Zbl 1365.65079) Full Text: DOI
Michiels, Wim; Hilhorst, Gijs; Pipeleers, Goele; Swevers, Jan Model order reduction for time-delay systems, with application to fixed-order \(\mathscr {H}_2\) optimal controller design. (English) Zbl 1349.93079 Witrant, Emmanuel (ed.) et al., Recent results on time-delay systems. Analysis and control. Selected papers based on the presentations at the 11th International Federation of Automatic Control, IFAC, workshop on time-delay systems, Genoble, France, February 4–6, 2013 and at the 52nd IEEE conference on decision and control, Florence, Italy, December 10–13, 2013. Cham: Springer (ISBN 978-3-319-26367-0/hbk; 978-3-319-26369-4/ebook). Advances in Delays and Dynamics 5, 45-66 (2016). MSC: 93B11 93C15 93C05 PDFBibTeX XMLCite \textit{W. Michiels} et al., Adv. Delays Dyn. 5, 45--66 (2016; Zbl 1349.93079) Full Text: DOI
Nechak, Lyès; Raynaud, Henri-François; Kulcsár, Caroline Model order reduction of random parameter-dependent linear systems. (English) Zbl 1378.93118 Automatica 55, 95-107 (2015). MSC: 93E03 93B17 93B11 93C41 93C05 PDFBibTeX XMLCite \textit{L. Nechak} et al., Automatica 55, 95--107 (2015; Zbl 1378.93118) Full Text: DOI
Zubov, N. E.; Mikrin, E. A.; Misrikhanov, M. Sh.; Proletarskii, A. V.; Ryabchenko, V. N. Reduction of large-scale dynamical systems by the Krylov subspaces method: analysis of approaches. (English. Russian original) Zbl 1327.93102 J. Comput. Syst. Sci. Int. 54, No. 2, 165-183 (2015); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2015, No. 2, 3-21 (2015). MSC: 93B11 93A15 93B40 93C15 93C05 PDFBibTeX XMLCite \textit{N. E. Zubov} et al., J. Comput. Syst. Sci. Int. 54, No. 2, 165--183 (2015; Zbl 1327.93102); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2015, No. 2, 3--21 (2015) Full Text: DOI
Baur, Ulrike; Benner, Peter; Feng, Lihong Model order reduction for linear and nonlinear systems: a system-theoretic perspective. (English) Zbl 1348.93075 Arch. Comput. Methods Eng. 21, No. 4, 331-358 (2014). MSC: 93B17 PDFBibTeX XMLCite \textit{U. Baur} et al., Arch. Comput. Methods Eng. 21, No. 4, 331--358 (2014; Zbl 1348.93075) Full Text: DOI
Šego, Vedran The hyperbolic Schur decomposition. (English) Zbl 1286.15029 Linear Algebra Appl. 440, 90-110 (2014). MSC: 15A63 15A21 PDFBibTeX XMLCite \textit{V. Šego}, Linear Algebra Appl. 440, 90--110 (2014; Zbl 1286.15029) Full Text: DOI
Van Beeumen, R.; Van Nimmen, K.; Lombaert, G.; Meerbergen, K. Model reduction for dynamical systems with quadratic output. (English) Zbl 1246.74024 Int. J. Numer. Methods Eng. 91, No. 3, 229-248 (2012). MSC: 74H15 74H45 PDFBibTeX XMLCite \textit{R. Van Beeumen} et al., Int. J. Numer. Methods Eng. 91, No. 3, 229--248 (2012; Zbl 1246.74024) Full Text: DOI
Mehrmann, Volker; Schröder, C.; Simoncini, Valeria An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems. (English) Zbl 1247.65050 Linear Algebra Appl. 436, No. 10, 4070-4087 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 65F18 65F50 PDFBibTeX XMLCite \textit{V. Mehrmann} et al., Linear Algebra Appl. 436, No. 10, 4070--4087 (2012; Zbl 1247.65050) Full Text: DOI
Benner, Peter; Embree, Mark; Lehoucq, Richard B.; Kelley, C. T. A mathematical biography of Danny C. Sorensen. (English) Zbl 1238.01104 Linear Algebra Appl. 436, No. 8, 2717-2724 (2012). MSC: 01A70 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 436, No. 8, 2717--2724 (2012; Zbl 1238.01104) Full Text: DOI
Yan, Boyuan; Li, Peng Reduced order modeling of passive and quasi-active dendrites for nervous system simulation. (English) Zbl 1446.92096 J. Comput. Neurosci. 31, No. 2, 247-271 (2011). MSC: 92B20 PDFBibTeX XMLCite \textit{B. Yan} and \textit{P. Li}, J. Comput. Neurosci. 31, No. 2, 247--271 (2011; Zbl 1446.92096)
Eid, Rudy; Castañé-Selga, Rosa; Panzer, Heiko; Wolf, Thomas; Lohmann, Boris Stability-preserving parametric model reduction by matrix interpolation. (English) Zbl 1302.93057 Math. Comput. Model. Dyn. Syst. 17, No. 4, 319-335 (2011). MSC: 93B11 93D05 93C15 PDFBibTeX XMLCite \textit{R. Eid} et al., Math. Comput. Model. Dyn. Syst. 17, No. 4, 319--335 (2011; Zbl 1302.93057) Full Text: DOI Link
Benner, Peter; Faßbender, Heike; Stoll, Martin A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process. (English) Zbl 1219.65040 Linear Algebra Appl. 435, No. 3, 578-600 (2011). Reviewer: R. Militaru (Craiova) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 435, No. 3, 578--600 (2011; Zbl 1219.65040) Full Text: DOI
Yousefi, Amirhossein; Lohmann, Boris A note on stability in model reduction. (English) Zbl 1167.93322 Int. J. Syst. Sci. 40, No. 3, 297-307 (2009). MSC: 93B11 93D99 PDFBibTeX XMLCite \textit{A. Yousefi} and \textit{B. Lohmann}, Int. J. Syst. Sci. 40, No. 3, 297--307 (2009; Zbl 1167.93322) Full Text: DOI
Frangos, Michalis; Jaimoukha, Imad M. Adaptive rational interpolation: Arnoldi and Lanczos-like equations. (English) Zbl 1293.93446 Eur. J. Control 14, No. 4, 342-354 (2008). MSC: 93C40 93B40 93B11 PDFBibTeX XMLCite \textit{M. Frangos} and \textit{I. M. Jaimoukha}, Eur. J. Control 14, No. 4, 342--354 (2008; Zbl 1293.93446) Full Text: DOI Link
Yousefi, A.; Lohmann, B. A parameterization of reduced stable models and controllers. (English) Zbl 1194.93039 Int. J. Control 81, No. 1, 146-155 (2008). MSC: 93B17 PDFBibTeX XMLCite \textit{A. Yousefi} and \textit{B. Lohmann}, Int. J. Control 81, No. 1, 146--155 (2008; Zbl 1194.93039) Full Text: DOI
Gugercin, Serkan An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems. (English) Zbl 1137.93006 Linear Algebra Appl. 428, No. 8-9, 1964-1986 (2008). MSC: 93A15 93B11 93D20 PDFBibTeX XMLCite \textit{S. Gugercin}, Linear Algebra Appl. 428, No. 8--9, 1964--1986 (2008; Zbl 1137.93006) Full Text: DOI
Genin, Yves; Vandendorpe, Antoine On the embedding of state space realizations. (English) Zbl 1116.93026 Math. Control Signals Syst. 19, No. 2, 123-149 (2007). MSC: 93B20 93C05 93C15 PDFBibTeX XMLCite \textit{Y. Genin} and \textit{A. Vandendorpe}, Math. Control Signals Syst. 19, No. 2, 123--149 (2007; Zbl 1116.93026) 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
Bai, Zhaojun; Skoogh, Daniel A projection method for model reduction of bilinear dynamical systems. (English) Zbl 1107.93012 Linear Algebra Appl. 415, No. 2-3, 406-425 (2006). Reviewer: Inge Troch (Wien) MSC: 93B11 93A30 93C10 PDFBibTeX XMLCite \textit{Z. Bai} and \textit{D. Skoogh}, Linear Algebra Appl. 415, No. 2--3, 406--425 (2006; Zbl 1107.93012) Full Text: DOI
Gugercin, Serkan; Antoulas, Athanasios C. Model reduction of large-scale systems by least squares. (English) Zbl 1112.93015 Linear Algebra Appl. 415, No. 2-3, 290-321 (2006). Reviewer: Andrea Bacciotti (Torino) MSC: 93B11 93C15 93D99 93C55 PDFBibTeX XMLCite \textit{S. Gugercin} and \textit{A. C. Antoulas}, Linear Algebra Appl. 415, No. 2--3, 290--321 (2006; Zbl 1112.93015) Full Text: DOI
Stykel, Tatjana Balanced truncation model reduction for semidiscretized Stokes equation. (English) Zbl 1102.65075 Linear Algebra Appl. 415, No. 2-3, 262-289 (2006). Reviewer: Piotr Matus (Minsk) MSC: 65K10 37N10 93A15 65M20 93B05 93B07 93B11 03C20 35Q30 35B37 PDFBibTeX XMLCite \textit{T. Stykel}, Linear Algebra Appl. 415, No. 2--3, 262--289 (2006; Zbl 1102.65075) Full Text: DOI
Lee, Herng-Jer; Chu, Chia-Chi; Feng, Wu-Shiung An adaptive-order rational Arnoldi method for model-order reductions of linear time-invariant systems. (English) Zbl 1105.93019 Linear Algebra Appl. 415, No. 2-3, 235-261 (2006). MSC: 93B11 93C15 93A15 PDFBibTeX XMLCite \textit{H.-J. Lee} et al., Linear Algebra Appl. 415, No. 2--3, 235--261 (2006; Zbl 1105.93019) Full Text: DOI
Jbilou, K. An Arnoldi based algorithm for large algebraic Riccati equations. (English) Zbl 1094.65038 Appl. Math. Lett. 19, No. 5, 437-444 (2006). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{K. Jbilou}, Appl. Math. Lett. 19, No. 5, 437--444 (2006; Zbl 1094.65038) Full Text: DOI
Salam, Ahmed On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms. (English) Zbl 1111.65038 Numer. Algorithms 39, No. 4, 437-462 (2005). Reviewer: Alan L. Andrew (Bundoora) MSC: 65F25 65F15 65F50 15A23 PDFBibTeX XMLCite \textit{A. Salam}, Numer. Algorithms 39, No. 4, 437--462 (2005; Zbl 1111.65038) Full Text: DOI
Watkins, David S. On Hamiltonian and symplectic Lanczos processes. (English) Zbl 1062.65047 Linear Algebra Appl. 385, 23-45 (2004). Reviewer: Alan L. Andrew (Bundoora) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{D. S. Watkins}, Linear Algebra Appl. 385, 23--45 (2004; Zbl 1062.65047) Full Text: DOI
Bai, Zhaojun Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. (English) Zbl 1012.65136 Appl. Numer. Math. 43, No. 1-2, 9-44 (2002). MSC: 65P10 37M15 PDFBibTeX XMLCite \textit{Z. Bai}, Appl. Numer. Math. 43, No. 1--2, 9--44 (2002; Zbl 1012.65136) Full Text: DOI
Sorensen, D. C.; Antoulas, A. C. The Sylvester equation and approximate balanced reduction. (English) Zbl 1023.93012 Linear Algebra Appl. 351-352, 671-700 (2002). Reviewer: L.Rodman (Williamsburg) MSC: 93B11 15A24 93B20 41A05 PDFBibTeX XMLCite \textit{D. C. Sorensen} and \textit{A. C. Antoulas}, Linear Algebra Appl. 351--352, 671--700 (2002; Zbl 1023.93012) Full Text: DOI
Antoulas, A. C.; Sorensen, D. C.; Zhou, Y. On the decay rate of Hankel singular values and related issues. (English) Zbl 1003.93024 Syst. Control Lett. 46, No. 5, 323-342 (2002). MSC: 93B60 93B11 15A18 15A24 PDFBibTeX XMLCite \textit{A. C. Antoulas} et al., Syst. Control Lett. 46, No. 5, 323--342 (2002; Zbl 1003.93024) Full Text: DOI
Bai, Zhaojun; Freund, Roland W. A partial Padé-via-Lanczos method for reduced-order modeling. (English) Zbl 0980.93012 Linear Algebra Appl. 332-334, No. 1-3, 139-164 (2001). Reviewer: Adhemar Bultheel (Leuven) MSC: 93B11 41A21 PDFBibTeX XMLCite \textit{Z. Bai} and \textit{R. W. Freund}, Linear Algebra Appl. 332--334, 139--164 (2001; Zbl 0980.93012) Full Text: DOI
Antoulas, A. C.; Sorensen, D. C. Lyapunov, Lanczos, and inertia. (English) Zbl 0997.65065 Linear Algebra Appl. 326, No. 1-3, 137-150 (2001). Reviewer: Raffela Pavani (Milano) MSC: 65F15 15A24 65F30 PDFBibTeX XMLCite \textit{A. C. Antoulas} and \textit{D. C. Sorensen}, Linear Algebra Appl. 326, No. 1--3, 137--150 (2001; Zbl 0997.65065) Full Text: DOI
Benner, Peter; Faßbender, Heike The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method. (English) Zbl 0935.65030 Linear Algebra Appl. 275-276, 19-47 (1998). MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Faßbender}, Linear Algebra Appl. 275--276, 19--47 (1998; Zbl 0935.65030) Full Text: DOI
Benner, Peter; Faßbender, Heike An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem. (English) Zbl 0884.65028 Linear Algebra Appl. 263, 75-111 (1997). Reviewer: A.Ruhe (Göteborg) MSC: 65F15 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Faßbender}, Linear Algebra Appl. 263, 75--111 (1997; Zbl 0884.65028) Full Text: DOI
Gallivan, K.; Grimme, E.; Van Dooren, P. A rational Lanczos algorithm for model reduction. (English) Zbl 0870.65053 Numer. Algorithms 12, No. 1-2, 33-63 (1996). Reviewer: G.Jumarie (Montréal) MSC: 65K10 93C15 93A99 65F15 PDFBibTeX XMLCite \textit{K. Gallivan} et al., Numer. Algorithms 12, No. 1--2, 33--63 (1996; Zbl 0870.65053) Full Text: DOI
Grimme, E. J.; Sorensen, D. C.; Van Dooren, P. Model reduction of state space systems via an implicitly restarted Lanczos method. (English) Zbl 0870.65052 Numer. Algorithms 12, No. 1-2, 1-31 (1996). Reviewer: G.Jumarie (Montréal) MSC: 65K10 93A99 93C15 65F15 PDFBibTeX XMLCite \textit{E. J. Grimme} et al., Numer. Algorithms 12, No. 1--2, 1--31 (1996; Zbl 0870.65052) Full Text: DOI