Algorithm 705

Algorithm 705: a Fortran-77 software package for solving the Sylvester matrix equation AXB T +CXD T =E. This paper documents a software package for solving the Sylvester matrix equation (1) AXBT + CXDT = e All quantities are real matrices; A and C are m x n; B and D are m x n; and X and E are m x n. The unknown is X. Two symmetric forms of Eq. (1) are treated separately for efficiency. They are the continuous-time symmetric Sylvester equation (2) AXET + EXAT + C = 0 and the discrete time equation (3) AXAT + C = 0, for which A, E, and C is symmetric. The software also provides a means for estimating the condition number of these three equations. The algorithms employed are more fully described in an accompanying paper.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Simoncini, V.: Computational methods for linear matrix equations (2016)
  2. Benner, Peter; Faßbender, Heike: On the numerical solution of large-scale sparse discrete-time Riccati equations (2011)
  3. Benner, Peter; Sima, Vasile; Slowik, Martin: Evaluation of the linear matrix equation solvers in SLICOT (2007)
  4. Hopkins, Tim: Remark on algorithm 705: A Fortran-77 software package for solving the Sylvester matrix equation $AXB^T+ CXD^T= E$ (2002)
  5. Jonsson, Isak; Kågström, Bo: Parallel two-sided Sylvester-type matrix equation solvers for SMP systems using recursive blocking (2002)
  6. Jonsson, Isak; Kågström, Bo: Recursive blocked algorithms for solving triangular systems. II: two-sided and generalized Sylvester and Lyapunov matrix equations (2002)
  7. Stykel, Tatjana: Numerical solution and perturbation theory for generalized Lyapunov equations (2002)
  8. Higham, Nicholas J.; Kim, Hyun-Min: Solving a quadratic matrix equation by newton’s method with exact line searches (2001)
  9. Van Loan, Charles F.: The ubiquitous Kronecker product (2000)
  10. Hodel, A.Scottedward; Misra, Pradeep: Least-squares approximate solution of overdetermined Sylvester equations (1997)
  11. Gardiner, Judith D.; Laub, Alan J.; Amato, James J.; Moler, Cleve B.: Solution of the Sylvester matrix equation $AXB^T+CXD^T=E$ (1992)
  12. Gardiner, Judith D.; Wette, Matthew R.; Laub, Alan J.; Amato, James J.; Moler, Cleve B.: Algorithm 705: A FORTRAN-77 software package for solving the Sylvester matrix equation $AXB^T+CXD^T=E$ (1992)