Numerical Analysis and Applications

, Volume 11, Issue 4, pp 293–297 | Cite as

Numerical Solution of the Discrete BHH-Equation in the Normal Case

  • Kh. D. IkramovEmail author
  • Yu. O. Vorontsov


It is known that the solution of the semilinear matrix equation \(X - A\overline X B = C\) can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. We propose a method for solving the original semilinear equation in the normal case that permits to almost halve the execution time for equations of order n = 3000 compared to the library function dlyap, which solves Stein equations in Matlab.


continuous- and discrete-time Sylvester equations BHH-equations Schur form conjugate-normal matrix Matlab function dlyap 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bevis, J.H., Hall, F.J., and Hartwig, R.H., Consimilarity and the Matrix Equation AX −XB = C, Proc. Third Auburn Matrix Theory Conference, Amsterdam: North-Holland, 1987, pp. 51–64.zbMATHGoogle Scholar
  2. 2.
    Zhou, B., Lam, J., and Duan, G.-R., Toward Solution ofMatrix Equation X = Af(X)B +C, Lin. Alg. Appl., 2011, vol. 435, no. 6, pp. 1370–1398.Google Scholar
  3. 3.
    Ikramov, Kh.D., Chislennoe reshenie matrichnykh uravnenii (Numerical Solution of Matrix Equations), Moscow: Nauka, 1984.zbMATHGoogle Scholar
  4. 4.
    Golub, G.H. and Van Loan, C.F., Matrix Computations, Baltimore, Maryland: Johns Hopkins University Press, 1983.Google Scholar
  5. 5.
    Ikramov, Kh.D., Normality Conditions for Linear Matrix Equations of the Stein Type, Dokl. Akad. Nauk, 2015, vol. 91, no. 1, pp. 50–52.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Ikramov, Kh.D., Normality Conditions for Semilinear Matrix Operators of the Stein Type, Num. Anal. Appl., 2015, vol. 8, no. 4, pp. 299–303.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.LomonosovMoscow State UniversityLeninskie GoryMoscowRussia
  2. 2.GlobusMedia Ltd.MoscowRussia

Personalised recommendations