Skip to main content
Log in

Solution of the matrix equation AX−XB=C

Lösung der Matrixgleichung AX−XB=C

  • Short Communications
  • Published:
Computing Aims and scope Submit manuscript

Abstract

In this paper a finite algebraic formula for the solution of the matrix equationAX−XB=C is derived. Based on it, a new direct algorithm is given.

Zusammenfassung

Angegeben wird eine algebraische Formel für die Lösung der GleichungAX−XB=C und ein auf ihr basierender Lösungsalgorithmus.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Gantmacher, F. R.: The theory of matrices. Gosud. Izdat. Techn.-Teor. Lit., Moscow (1954).

    Google Scholar 

  2. Kreisselmeier, G.: A solution of the bilinear matrix equationAY+YB=−Q. SIAM. J. Appl. Math., Vol. 23, No. 3, Nov. 1972.

  3. Jones, J. Jr., Lew, C.: Solutions of the Lyapunov matrix equationBX−XA=C. IEEE Trans. Automat Contr.AC-27, 464–466 (1982).

    Google Scholar 

  4. Golub, G. H., Nash, S., Van Loan, C.: A Hessenberg-Schur method for the problemAX+XB=C. IEEE Trans. Automat Contr.AC-24, 909–913 (1979).

    Google Scholar 

  5. Hoskins, W. D., Meek, D. S., Walton, D. J.: The numerical solution of the matrix equationXA+AY=F. BIT17, 184–190 (1977).

    Google Scholar 

  6. Deif, A. S.: Advanced matrix theory for scientists and engineers. First published in 1982 by ABACUS Press.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tongxing, L. Solution of the matrix equation AX−XB=C. Computing 37, 351–355 (1986). https://doi.org/10.1007/BF02251092

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02251092

AMS Subject Classification

Key words

Navigation