Algorithm 705; a FORTRAN-77 software package for solving the Sylvester matrix equation AXBT + CXDT = E

ABSTRACT

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 [3].

REFERENCES

• 1: DO~GARRA, J. J., Bv~en, J. R., MOLER, C. B., A~D STEW^RT, G W. LINPACK Users' Guide Society for Industrial and Apphed Mathematics, Philadelphm, Pa., 1979.
• 2: GARSOW, B. S., BOYLE, J. M., DO~GARRA, J. J, A~D MOLER, C B. Matrix Etgensystem Routmes-EISPACK Guide Extension, Vol. 51 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1977.
• 3: Judith D. Gardiner , Alan J. Laub , James J. Amato , Cleve B. Moler, Solution of the Sylvester matrix equation AXBT + CXDT = E, ACM Transactions on Mathematical Software (TOMS), v.18 n.2, p.223-231, June 1992 [doi>10.1145/146847.146929]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Conditioning
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Efficiency; Algorithm design and analysis; Reliability and robustness

General Terms:
Algorithms, Performance