LYAPACK swMATH ID: 12624 Software Authors: Thilo Penzl Description: LYAPACK A MATLAB Toolbox for Large Lyapunov and Riccati Equations, Model Reduction Problems, and Linear–Quadratic Optimal Control Problems Users ’ Guide (Version 1.0). Control theory is one of the most rapidly developing disciplines of mathematics and engineering in the second half of the 20th century. In the past decade, implementations of numerically robust algorithms for many types of dense problems in control theory have become available in software packages, such as SLICOT [7]. However, little research has been done on efficient numerical methods for control problems related to large sparse or structured dynamical systems before 1990. In the last few years, quite a number of approaches for several types of large control problems have been proposed, but, at present, it is often not clear, which of them are the more promising ones. It is needless to say that there is little software for large control problems available. In this situation, the author took the opportunity to implement the software package LYAPACK (“Lyapunov Package”), which covers one particular approach to a class of large problems in control theory. An efficient ADI-based solver for large Lyapunov equations is the “workhorse ” of LYAPACK, which also contains implementations of two model reduction methods and modifications of the Newton method for the solution of large Riccati equations and linear-quadratic optimal control problems. .. Homepage: https://www.tu-chemnitz.de/sfb393/lyapack/ Dependencies: Matlab Related Software: Algorithm 432; Matlab; benchmodred; SparseMatrix; SLICOT; mctoolbox; MESS; RICPAC; MatrixMarket; TensorToolbox; sssMOR; CMRH; mftoolbox; ABLE; Algorithm 705; ARPACK; CAREX; LAPACK; toms/782; RRQR Cited in: 67 Publications all top 5 Cited by 93 Authors 17 Benner, Peter 14 Jbilou, Khalide 12 Saak, Jens 9 Bentbib, Abdeslem Hafid 6 Heyouni, Mohammed 6 Simoncini, Valeria 4 Kaouane, Yassine 4 Mena, Hermann 4 Sadek, El Mostafa 4 Weichelt, Heiko K. 3 Barkouki, Houda 3 Truhar, Ninoslav 2 Bouhamidi, Abderrahman 2 Druskin, Vladimir 2 El-Halouy, Smahane 2 Elbouyahyaoui, Lakhdar 2 Hached, Mehrez 2 Kressner, Daniel 2 Kürschner, Patrick 2 Li, Rencang 2 Mehrmann, Volker 2 Penzl, Thilo 2 Poloni, Federico Giovanni 2 Pulch, Roland 2 Sadek, Lakhlifa 2 Stykel, Tatjana 1 Abidi, O. 1 Addam, Mohamed 1 Ahmad, Mian Ilyas 1 Badía, José M. 1 Bänsch, Eberhard 1 Baur, Ulrike 1 Bini, Dario Andrea 1 Braun, Philipp 1 Bui-Thanh, Tan 1 Bujanović, Zvonimir 1 Chen, Qi-Xing 1 De los Reyes, Juan Carlos 1 Du, Xin 1 Faßbender, Heike 1 Ghattas, Omar N. 1 Hamadi, M. A. 1 Heinkenschloss, Matthias 1 Hernández, Erwin 1 Huang, Guang-Xin 1 Iannazzo, Bruno 1 Kalise, Dante 1 Knizhnerman, Leonid 1 Lang, Norman 1 Li, Dongping 1 Lin, Yiding 1 Liu, Renyun 1 Massoudi, Arash 1 Mayo, Rafael 1 Meini, Beatrice 1 Messaoudi, Abderrahim 1 Monsalve, Marlliny 1 Morris, Kirsten A. 1 Narayan, Akil C. 1 Navasca, Carmeliza 1 Opmeer, Mark R. 1 Ostermann, Alexander 1 Pfurtscheller, Lena-Maria 1 Piazzola, Chiara 1 Plešinger, Martin 1 Quintana-Ortí, Enrique S. 1 Quintana-Ortí, Gregorio 1 Ratnani, Ahmed 1 Reis, Timo 1 Remón, Alfredo 1 Ren, Limin 1 Saberi Movahed, Farid 1 Schieweck, Friedhelm 1 Schröder, Christian 1 Skrzypacz, Piotr 1 Sreeram, Victor 1 Stoll, Martin 1 Szyld, Daniel B. 1 Tabaa, Khalid 1 Tajaddini, Azita 1 Talibi Alaoui, Hamad 1 Talibi, Alaoui Hamad 1 Tobler, Christine 1 Tomljanović, Zoran 1 Veselić, Krešimir 1 Watkins, David S. 1 Willcox, Karen E. 1 Xie, Yajun 1 Yin, Feng 1 Yin, Minhua 1 Zaslavsky, Mikhail 1 Zhang, Xiuying 1 Zulfiqar, Umair all top 5 Cited in 35 Serials 6 Numerical Linear Algebra with Applications 4 Journal of Computational and Applied Mathematics 4 Numerical Algorithms 4 SIAM Journal on Scientific Computing 3 SIAM Journal on Matrix Analysis and Applications 3 Journal of Scientific Computing 3 Linear Algebra and its Applications 2 Applied Mathematics and Computation 2 Systems & Control Letters 2 Applied Numerical Mathematics 2 Computational and Applied Mathematics 2 Advances in Computational Mathematics 2 Journal of Numerical Mathematics 2 Journal of Applied Mathematics and Computing 2 GAMM-Mitteilungen 2 PAMM. Proceedings in Applied Mathematics and Mechanics 1 IMA Journal of Numerical Analysis 1 Journal of Computational Physics 1 Calcolo 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 Journal of Global Optimization 1 SIAM Review 1 Computational Optimization and Applications 1 Applicationes Mathematicae 1 ETNA. Electronic Transactions on Numerical Analysis 1 Optimization Methods & Software 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Discrete and Continuous Dynamical Systems. Series S 1 Numerical Algebra, Control and Optimization 1 Journal of Applied Analysis and Computation 1 Mathematics 1 Journal of Mathematical Modeling 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Fundamentals of Algorithms all top 5 Cited in 15 Fields 57 Numerical analysis (65-XX) 32 Linear and multilinear algebra; matrix theory (15-XX) 27 Systems theory; control (93-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 4 Ordinary differential equations (34-XX) 4 Fluid mechanics (76-XX) 3 Partial differential equations (35-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 1 Mathematical logic and foundations (03-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year