Loewner swMATH ID: 17575 Software Authors: Antoulas, A.C. Description: The Loewner framework and transfer functions of singular/rectangular systems. A connection is established between the Loewner framework for model reduction and the generalized inverses of singular and rectangular matrices. In this context both the Moore-Penrose and the Drazin inverses are involved. As a consequence this approach yields transfer functions for singular and rectangular systems. Thus the Loewner framework constitutes a natural and direct way for constructing models from measured input/output data. Homepage: http://www.sciencedirect.com/science/article/pii/S0893965915003122 Keywords: model reduction; data-driven model reduction; rational interpolation; interpolatory model reduction; Loewner framework; Moore-Penrose generalized inverse; Drazin generalized inverse; transfer functions; singular systems; rectangular systems Related Software: redbKIT; benchmodred; AAA; RKToolbox; Matlab; Chebfun; rbMIT; MESS; HODMD; Eigtool; NLEVP; mctoolbox; GitHub; emgr; SINDy; FEAST; CVX; GRANSO; Algorithm 432; Hm-toolbox Cited in: 77 Documents all top 5 Cited by 101 Authors 14 Antoulas, Athanasios C. 12 Gugercin, Serkan 11 Gosea, Ion Victor 10 Peherstorfer, Benjamin 9 Benner, Peter 7 Willcox, Karen E. 6 Rapisarda, Paolo 5 Beattie, Christopher A. 5 Goyal, Pawan 4 Krämer, Boris 3 Drmač, Zlatko 3 Ionita, Antonio C. 3 Poussot-Vassal, Charles 3 Unger, Benjamin 2 Dede’, Luca 2 Demourant, Fabrice 2 Embree, Mark 2 Heinkenschloss, Matthias 2 Karachalios, Dimitrios S. 2 Karasözen, Bülent 2 Kergus, Pauline 2 Lefteriu, Sanda 2 Petreczky, Mihály 2 Pontes Duff, Igor 2 Pradovera, Davide 2 Quarteroni, Alfio M. 2 Regazzoni, Francesco 2 Schulze, Philipp 2 Uy, Wayne Isaac Tan 2 Uzunca, Murat 2 Werner, Steffen W. R. 1 Ahuja, Kapil 1 Akçay, Hüseyin 1 Astolfi, Alessandro 1 Ball, Joseph Anthony 1 Bencherki, Fethi 1 Bolotnikov, Vladimir 1 Borcea, Liliana 1 Borggaard, Jeff T. 1 Breiten, Tobias 1 Brennan, Michael C. 1 Brevis, Ignacio 1 Cao, Xingang 1 Carracedo Rodriguez, Andrea 1 Cherifi, Karim 1 Cui, Tiangang 1 Damle, Anil 1 Diaz, Alejandro N. 1 Druskin, Vladimir 1 Güttel, Stefan 1 Haasdonk, Bernard 1 Hassanzadeh, Pedram 1 Heiland, Jan 1 Hijazi, Saddam 1 Hund, Manuela 1 Iftime, Orest V. 1 Ionescu, Tudor Corneliu 1 Ioniţă, A. Cosmin 1 Jiang, Yaolin 1 Jiang, Zhong-Ping 1 Khodabakhshi, Parisa 1 Khodkar, M. A. 1 Li, Yanpeng 1 Mamonov, Alexander V. 1 Marzouk, Youssef M. 1 Maubach, Joseph M. L. 1 Mitchell, Tim 1 Mlinarić, Petar 1 Mola, Andrea 1 Moskow, Shari 1 Muga, Ignacio 1 Nakatsukasa, Yuji 1 Necoara, Ion 1 Nobile, Fabio 1 Palitta, Davide 1 Rantzer, Anders 1 Rozza, Gianluigi 1 Saak, Jens 1 Sawant, Nihar 1 Scarciotti, Giordano 1 Schilders, Wil H. A. 1 Sharma, Harsh 1 Singh, Navneet Pratap 1 Son, Nguyen Thanh 1 Sootla, Aivar 1 Sou, Kin Cheong 1 Stabile, Giovanni 1 Stykel, Tatjana 1 Tomljanović, Zoran 1 Townsend, Alex 1 Trefethen, Lloyd Nicholas 1 Türkay, Semiha 1 van der Zee, Kristoffer George 1 Vuillemin, Pierre 1 Wang, Zhu 1 Weiland, Siep 1 Wilber, Heather 1 Yang, Ping 1 Yıldız, Süleyman 1 Zaslavsky, Mikhail ...and 1 more Authors all top 5 Cited in 25 Serials 13 SIAM Journal on Scientific Computing 6 Computer Methods in Applied Mechanics and Engineering 5 Advances in Computational Mathematics 4 Automatica 4 Systems & Control Letters 3 Journal of Computational Physics 3 Journal of Scientific Computing 2 International Journal of Control 2 SIAM Review 2 ETNA. Electronic Transactions on Numerical Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Computers & Mathematics with Applications 1 Inverse Problems 1 Applied Mathematics and Computation 1 Mathematics and Computers in Simulation 1 SIAM Journal on Control and Optimization 1 SIAM Journal on Numerical Analysis 1 Physica D 1 Applied Mathematics Letters 1 Multidimensional Systems and Signal Processing 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 European Journal of Control 1 SIAM Journal on Applied Dynamical Systems 1 Nonlinear Analysis. Hybrid Systems all top 5 Cited in 20 Fields 53 Systems theory; control (93-XX) 30 Numerical analysis (65-XX) 14 Approximations and expansions (41-XX) 8 Partial differential equations (35-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Computer science (68-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Fluid mechanics (76-XX) 4 Functions of a complex variable (30-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year