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)].

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References in zbMATH (referenced in 202 articles , 1 standard article )

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  1. Jarlebring, Elias; Poloni, Federico: Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning (2019)
  2. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)
  3. Abidi, O.; Jbilou, K.: Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems (2018)
  4. Addam, Mohamed; Elbouyahyaoui, Lakhdar; Heyouni, Mohammed: On Hessenberg type methods for low-rank Lyapunov matrix equations (2018)
  5. Benner, Peter; Goyal, Pawan; Gugercin, Serkan: (\mathcalH_2)-quasi-optimal model order reduction for quadratic-bilinear control systems (2018)
  6. Cheng, Xiaodong; Scherpen, Jacquelien M. A.: Clustering approach to model order reduction of power networks with distributed controllers (2018)
  7. Fasi, Massimiliano; Higham, Nicholas J.: Multiprecision algorithms for computing the matrix logarithm (2018)
  8. Hached, M.; Jbilou, K.: Numerical solutions to large-scale differential Lyapunov matrix equations (2018)
  9. He, Qixiang; Hou, Liangshao; Zhou, Jieyong: The solution of fuzzy Sylvester matrix equation (2018)
  10. Hernández-Verón, M. A.; Romero, Natalia: Solving symmetric algebraic Riccati equations with high order iterative schemes (2018)
  11. Huroyan, Vahan; Lerman, Gilad: Distributed robust subspace recovery (2018)
  12. Kürschner, Patrick: Balanced truncation model order reduction in limited time intervals for large systems (2018)
  13. Li, Xu; Huo, Hai-Feng; Yang, Ai-Li: Preconditioned HSS iteration method and its non-alternating variant for continuous Sylvester equations (2018)
  14. Luo, Quanbing; Liang, Dong; Ren, Ting; Zhang, Jian: Calculation of critical parameters for spontaneous combustion for some complex geometries using an indirect numerical method (2018)
  15. Massei, Stefano; Palitta, Davide; Robol, Leonardo: Solving rank-structured Sylvester and Lyapunov equations (2018)
  16. Nazari, A. M.; Mollaghasemi, S.; Bahmani, F.: On the solving matrix equations by using the spectral representation (2018)
  17. Palitta, Davide; Simoncini, Valeria: Numerical methods for large-scale Lyapunov equations with symmetric banded data (2018)
  18. Palitta, Davide; Simoncini, Valeria: Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations (2018)
  19. Rashidinia, J.; Khasi, M.; Fasshauer, G. E.: A stable Gaussian radial basis function method for solving nonlinear unsteady convection-diffusion-reaction equations (2018)
  20. Baars, S.; Viebahn, J. P.; Mulder, T. E.; Kuehn, C.; Wubs, F. W.; Dijkstra, H. A.: Continuation of probability density functions using a generalized Lyapunov approach (2017)

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