Algorithm 432

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)].

References in zbMATH (referenced in 241 articles , 1 standard article )

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  1. Massei, Stefano; Robol, Leonardo: Rational Krylov for Stieltjes matrix functions: convergence and pole selection (2021)
  2. Bini, Dario A.; Meini, Beatrice; Meng, Jie: Solving quadratic matrix equations arising in random walks in the quarter plane (2020)
  3. Chan, N. H.; Cheung, Simon K. C.; Wong, Samuel P. S.: Inference for the degree distributions of preferential attachment networks with zero-degree nodes (2020)
  4. Chen, Minhong; Kressner, Daniel: Recursive blocked algorithms for linear systems with Kronecker product structure (2020)
  5. Devi, Vinita; Maurya, Rahul Kumar; Singh, Somveer; Singh, Vineet Kumar: Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions (2020)
  6. Fasi, Massimiliano; Iannazzo, Bruno: Substitution algorithms for rational matrix equations (2020)
  7. Hached, M.; Jbilou, K.: Numerical methods for differential linear matrix equations via Krylov subspace methods (2020)
  8. Kürschner, Patrick; Freitag, Melina A.: Inexact methods for the low rank solution to large scale Lyapunov equations (2020)
  9. Lui, S. H.; Nataj, Sarah: Chebyshev spectral collocation in space and time for the heat equation (2020)
  10. Dehghan, Mehdi; Shirilord, Akbar: The double-step scale splitting method for solving complex Sylvester matrix equation (2019)
  11. Dehghan, Mehdi; Shirilord, Akbar: A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation (2019)
  12. Hossain, M. Sumon; Uddin, M. Monir: Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations (2019)
  13. Jarlebring, Elias; Poloni, Federico: Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning (2019)
  14. Kressner, Daniel: A Krylov subspace method for the approximation of bivariate matrix functions (2019)
  15. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)
  16. Pickering, Andrew; Gordoa, Pilar R.; Wattis, Jonathan A. D.: The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases (2019)
  17. Zadeh, Najmeh Azizi; Tajaddini, Azita; Wu, Gang: Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations (2019)
  18. Abidi, O.; Jbilou, K.: Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems (2018)
  19. Addam, Mohamed; Elbouyahyaoui, Lakhdar; Heyouni, Mohammed: On Hessenberg type methods for low-rank Lyapunov matrix equations (2018)
  20. Benner, Peter; Goyal, Pawan; Gugercin, Serkan: (\mathcalH_2)-quasi-optimal model order reduction for quadratic-bilinear control systems (2018)

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