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Algorithms for Solving Nonhomogeneous Generalized Sylvester Matrix Equations

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  • Ehab A. El-Sayed
  • Eid E. El Behady

Abstract

This paper considers a new method to solve the first-order and second-order nonhomogeneous generalized Sylvester matrix equations and , respectively, where , and are the arbitrary real known matrices and and are the matrices to be determined. An explicit solution for these equations is proposed, based on the orthogonal reduction of the matrix to an upper Hessenberg form . The technique is very simple and does not require the eigenvalues of matrix to be known. The proposed method is illustrated by numerical examples.

Suggested Citation

  • Ehab A. El-Sayed & Eid E. El Behady, 2020. "Algorithms for Solving Nonhomogeneous Generalized Sylvester Matrix Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-5, March.
    • Handle: RePEc:hin:jnlmpe:1549520
    DOI: 10.1155/2020/1549520
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