Skip to main content
SpringerLink
Log in

An efficient algorithm for the generalized centro-symmetric solution of matrix equation A X B = C

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this paper, an iterative algorithm is constructed for solving linear matrix equation AXB = C over generalized centro-symmetric matrix X. We show that, by this algorithm, a solution or the least-norm solution of the matrix equation AXB = C can be obtained within finite iteration steps in the absence of roundoff errors; we also obtain the optimal approximation solution to a given matrix X 0 in the solution set of which. In addition, given numerical examples show that the iterative method is efficient.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Golub, G.H., Van Loan, C.F.: Matrix computations [M]. John Hopkins University Press, Baltimore, MD (1996)

    Google Scholar 

  2. Zhou, F.Z., Hu, X.Y., Zhang, L.: The solvability conditions for the inverse eigenvalue problems of centro-symmetric matrices. Linear Algebra Appl. 364, 147–160 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dai, H.: On the symmetric solutions of linear matrix equations. Linear Algebra Appl. 131, 1–7 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chu, K.E.: Symmetric solutions of linear matrix equations by matrix decompositions. Linear Algebra Appl. 119, 35–50 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  5. Mitra, S.K.: Common solutions to a pair of linear matrix equations A 1 XB 1 = C 1, A 2 XB 2 = C 2. Proc. Camb. Philos. Soc. 74, 213–216 (1973)

    Article  MATH  Google Scholar 

  6. Peng, X.Y., Hu, X.Y., Zhang, L.: The reflexive and anti-reflexive solutions of the matrix equation A * XB = C. J. Comput. Appl. Math. 200, 749–760 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Peng, Y.X., Hu, X.Y., Zhang, L.: An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C. Appl. Math. Comput. 160, 763–777 (2005)

    MATH  MathSciNet  Google Scholar 

  8. Peng, Y.X., Hu, X.Y., Zhang, L.: An iteration method for symmetric solutions and optimal approximation solution of the system of matrix equations A 1 XB 1 = C 1, A 2 XB 2 = C 2. Appl. Math. Comput. 183, 1127–1137 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Peng, Z.Y.: An iterative method for the least-squares symmetric solution of the linear matrix equation AXB = C. Appl. Math. Comput. 170, 711–723 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Xie, D.X., Hu, X.Y., Sheng, Y.P.: The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations. Linear Algebra Appl. 418, 142–152 (2006)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China

    Mao-lin Liang, Chuan-hua You & Li-fang Dai

  2. College of Mathematics–Physics and Information Science, Tianshui Normal University, Tianshui, Gansu, 741001, People’s Republic of China

    Mao-lin Liang & Li-fang Dai

Authors
  1. Mao-lin Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuan-hua You
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li-fang Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mao-lin Liang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liang, Ml., You, Ch. & Dai, Lf. An efficient algorithm for the generalized centro-symmetric solution of matrix equation A X B = C . Numer Algor 44, 173–184 (2007). https://doi.org/10.1007/s11075-007-9097-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-007-9097-z

Keywords

Search

Navigation