## Algorithm 432

 swMATH ID: 25817 Software Authors: Bartels, R. H.; Stewart, G. W. Description: Algorithm 432: Solution of the matrix equation AX + XB = C [F4]. The following programs are a collection of Fortran IV subroutines to solve the matrix equation AX+XB=C(1) where A, B, and C are real matrices of dimensions m×m, n×n, and m×n, respectively. Additional subroutines permit the efficient solution of the equation A T X+XA=C, where C is symmetric. Equation (1) has applications to the direct solution of discrete Poisson equations [W. G. Bickley and J. McNamee, Philos. Trans. R. Soc. Lond., Ser. A 252, 69–131 (1960; Zbl 0092.13001)]. Homepage: https://dl.acm.org/citation.cfm?doid=361573.361582 Keywords: linear algebra; matrices; linear equations Related Software: mctoolbox; Matlab; LYAPACK; LAPACK; mftoolbox; RICPAC; IRAM; eigs; benchmodred; MATLAB expm; SLICOT; CTLEX; SCASY; MPI; BLAS; ScaLAPACK; IFISS; CAREX; ARPACK; CSparse Cited in: 251 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Algorithm 432: Solution of the matrix equation $$AX + XB = C$$. Zbl 1372.65121
Bartels, R. H.; Stewart, G. W.
1972
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### Cited by 395 Authors

 16 Jbilou, Khalide 11 Simoncini, Valeria 10 Benner, Peter 6 Bouhamidi, Abderrahman 6 Palitta, Davide 5 Hached, Mehrez 5 Kressner, Daniel 5 Kürschner, Patrick 5 Toutounian, Faezeh 4 Hernández, Vicente G. 4 Heyouni, Mohammed 4 Higham, Nicholas J. 4 Ibáñez González, Jacinto Javier 4 Li, Rencang 4 Saak, Jens 3 Arias, Enrique 3 Bentbib, Abdeslem Hafid 3 Damm, Tobias 3 Dehghan Takht Fooladi, Mehdi 3 Diao, Huaian 3 Fasi, Massimiliano 3 Hernández-Verón, Miguel Ángel 3 Jarlebring, Elias 3 Kaabi, Amer 3 Kerayechian, Asghar 3 Khojasteh Salkuyeh, Davod 3 Massei, Stefano 3 Peinado, Jesús 3 Reichel, Lothar 3 Robol, Leonardo 3 Romero, Natalia 3 Song, Chongmin 3 Truhar, Ninoslav 3 Van Dooren, Paul M. 3 Wang, Xiang 3 Wei, Yimin 3 Wolf, John P. 3 Xu, Shufang 2 Bean, Nigel G. 2 Borno, I. 2 Breiten, Tobias 2 Cardoso, João R. 2 Chun, Hon M. 2 Datta, Karabi 2 Demmel, James Weldon 2 Dopico, Froilán M. 2 Ferreira, Carla 2 Fu, Yun 2 Gavrilyuk, Ivan P. 2 Giesl, Peter 2 Gugercin, Serkan 2 Guo, Chun-Hua 2 Hafstein, Sigurður Freyr 2 Hammarling, Sven J. 2 Harker, Matthew 2 Hashemi, Behnam 2 Hodel, A. Scottedward 2 Iannazzo, Bruno 2 Jonckheere, Edmond A. 2 Kit, Dmitry 2 Levenberg, Norman jun. 2 Lin, Yiqin 2 Liu, Zhongyun 2 Lv, Quanyi 2 Meerbergen, Karl 2 O’Leary, Paul 2 O’Reilly, Małgorzata M. 2 Penzl, Thilo 2 Plestenjak, Bor 2 Poloni, Federico Giovanni 2 Quintana-Ortí, Enrique S. 2 Raydan, Marcos 2 Sadek, El Mostafa 2 Shao, Ming 2 Shirilord, Akbar 2 Sorensen, Danny C. 2 Tani, Mattia 2 Taylor, Peter Gerrard 2 Turner, James D. 2 Wachspress, Eugene L. 2 Xiao, Manyu 2 Xue, Jungong 2 Zhang, Yulin 1 Abidi, O. 1 Absil, Pierre-Antoine 1 Addam, Mohamed 1 Agoujil, Said 1 Al-Smadi, Mohammed H. 1 Amodei, Luca 1 Ananiadou, Sophia 1 Andrei, Raluca 1 Antoulas, Athanasios C. 1 Baars, Sven 1 Bahmani, Fatemeh 1 Bai, Zhaojun 1 Bakkaloǧlu, Bertan 1 Bao, Liang 1 Bartels, Richard Harold 1 Baur, Ulrike 1 Benahmed, Boubakeur ...and 295 more Authors
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### Cited in 84 Serials

 30 Linear Algebra and its Applications 19 Applied Mathematics and Computation 14 Computers & Mathematics with Applications 10 Journal of Computational and Applied Mathematics 8 BIT 8 Numerical Algorithms 7 Numerische Mathematik 7 Systems & Control Letters 7 Applied Numerical Mathematics 7 SIAM Journal on Scientific Computing 7 Numerical Linear Algebra with Applications 7 ETNA. Electronic Transactions on Numerical Analysis 6 Automatica 6 SIAM Journal on Matrix Analysis and Applications 5 Journal of Computational Physics 4 Computer Methods in Applied Mechanics and Engineering 4 Mathematics of Computation 4 Computational and Applied Mathematics 4 Advances in Computational Mathematics 3 Journal of the Franklin Institute 3 Circuits, Systems, and Signal Processing 2 Journal of Mathematical Analysis and Applications 2 Computing 2 Journal of Optimization Theory and Applications 2 Theoretical Computer Science 2 Mathematical and Computer Modelling 2 MCSS. Mathematics of Control, Signals, and Systems 2 Journal of Scientific Computing 2 Journal of Global Optimization 2 Computational Optimization and Applications 2 International Journal of Computer Vision 2 ELA. The Electronic Journal of Linear Algebra 2 Mathematical Problems in Engineering 2 European Journal of Control 2 Soft Computing 2 Journal of Applied Mathematics and Computing 2 BIT. Nordisk Tidskrift for Informationsbehandling 1 Archive for Rational Mechanics and Analysis 1 Computer Physics Communications 1 International Journal of Engineering Science 1 Information Processing Letters 1 Journal of Mathematical Biology 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Optimization 1 Integral Equations and Operator Theory 1 Journal of Econometrics 1 Journal of Multivariate Analysis 1 Kybernetika 1 Meccanica 1 Applied Mathematics and Mechanics. (English Edition) 1 Physica D 1 Parallel Computing 1 Applied Mathematics Letters 1 Computational Statistics 1 Communications of the ACM 1 International Journal of Computer Mathematics 1 SIAM Review 1 Stochastic Processes and their Applications 1 Journal of Mathematical Imaging and Vision 1 Applicationes Mathematicae 1 Turkish Journal of Mathematics 1 The Journal of Fourier Analysis and Applications 1 Nonlinear Dynamics 1 Vietnam Journal of Mathematics 1 Abstract and Applied Analysis 1 Journal of Shanghai University 1 Discrete Dynamics in Nature and Society 1 Methodology and Computing in Applied Probability 1 The ANZIAM Journal 1 Journal of Applied Mathematics 1 Portugaliae Mathematica. Nova Série 1 Journal of Machine Learning Research (JMLR) 1 Mediterranean Journal of Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Acta Mechanica Sinica 1 SIAM Journal on Imaging Sciences 1 Algorithms 1 Science China. Mathematics 1 Asian Journal of Control 1 Numerical Algebra, Control and Optimization 1 Journal of Applied Analysis and Computation 1 Journal of Linear and Topological Algebra 1 Nonlinear Analysis. Theory, Methods & Applications 1 Open Mathematics
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### Cited in 33 Fields

 186 Numerical analysis (65-XX) 147 Linear and multilinear algebra; matrix theory (15-XX) 51 Systems theory; control (93-XX) 17 Partial differential equations (35-XX) 16 Ordinary differential equations (34-XX) 11 Computer science (68-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Operations research, mathematical programming (90-XX) 7 Probability theory and stochastic processes (60-XX) 7 Statistics (62-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Operator theory (47-XX) 5 Mechanics of deformable solids (74-XX) 5 Fluid mechanics (76-XX) 5 Information and communication theory, circuits (94-XX) 4 Approximations and expansions (41-XX) 4 Mechanics of particles and systems (70-XX) 2 Real functions (26-XX) 2 Sequences, series, summability (40-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)