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 246 articles , 1 standard article )

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  1. Delkhosh, Mehdi; Parand, Kourosh: A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations (2021)
  2. Langer, Ulrich; Zank, Marco: Efficient direct space-time finite element solvers for parabolic initial-boundary value problems In anisotropic Sobolev spaces (2021)
  3. Li, Sheng-Kun; Wang, Mao-Xiao; Liu, Gang: A global variant of the COCR method for the complex symmetric Sylvester matrix equation (AX+XB=C) (2021)
  4. Massei, Stefano; Robol, Leonardo: Rational Krylov for Stieltjes matrix functions: convergence and pole selection (2021)
  5. Palitta, Davide: Matrix equation techniques for certain evolutionary partial differential equations (2021)
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  7. 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)
  8. Chen, Minhong; Kressner, Daniel: Recursive blocked algorithms for linear systems with Kronecker product structure (2020)
  9. 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)
  10. Fasi, Massimiliano; Iannazzo, Bruno: Substitution algorithms for rational matrix equations (2020)
  11. Hached, M.; Jbilou, K.: Numerical methods for differential linear matrix equations via Krylov subspace methods (2020)
  12. Kürschner, Patrick; Freitag, Melina A.: Inexact methods for the low rank solution to large scale Lyapunov equations (2020)
  13. Lui, S. H.; Nataj, Sarah: Chebyshev spectral collocation in space and time for the heat equation (2020)
  14. Palitta, Davide; Simoncini, Valeria: Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equations (2020)
  15. Dehghan, Mehdi; Shirilord, Akbar: The double-step scale splitting method for solving complex Sylvester matrix equation (2019)
  16. Dehghan, Mehdi; Shirilord, Akbar: A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation (2019)
  17. 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)
  18. Jarlebring, Elias; Poloni, Federico: Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning (2019)
  19. Kressner, Daniel: A Krylov subspace method for the approximation of bivariate matrix functions (2019)
  20. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)

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