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Journals / Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 7 Sayı: 1

On Solution of Generalized Sylvester Transpose Matrix Equation Using Symmetric – Skew Symmetric Splitting Method

Genelleştirilmiş Sylvester Transpoz Matris Denkleminin Simetrik – Ters Simetrik Ayrışım Metodu ile Çözümü

Murat Sarduvan(SAKARYA ÜNİVERSİTESİ)0000-0001-7049-8922
Esra Kaplan(SAKARYA ÜNİVERSİTESİ)0000-0002-1872-1987
Pages
319–328
Publication Date
2020-06-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Lastly, an example is given to illustrate the performance of the SSS method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, Symmetric-Skew Symmetric Splitting (SSS) method is introduced to solve the system of linear equations Ax=b.
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Key Findings & Data:Then, the solution of AXB+CXD+EX T F=M generalized Sylvester transpose matrix equation is established by using this method.
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Conclusion & Impact:Lastly, an example is given to illustrate the performance of the SSS method.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:SSS metodu · Genelleştirilmiş Sylvester transpoz matris denklemi · Kronecker çarpım

Abstract

In this study, Symmetric-Skew Symmetric Splitting (SSS) method is introduced to solve the system of linear equations Ax=b. Then, the solution of AXB+CXD+EX T F=M generalized Sylvester transpose matrix equation is established by using this method. Lastly, an example is given to illustrate the performance of the SSS method.

Özet

Bu çalışmada Ax=b lineer denklem sisteminin çözümü için Simetrik-Ters Simetrik Ayrışım (SSS) metodu tanıtıldı. Daha sonra AXB+CXD+EX T F=M genelleştirilmiş Sylvester Transpoze matris denkleminin çözümü bu metot kullanılarak ortaya konuldu. Son olarak SSS metodunun performansını resmeden sayısal bir örnek verildi.

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Cite This Article

Sarduvan, M., Kaplan, E. (2020). On Solution of Generalized Sylvester Transpose Matrix Equation Using Symmetric – Skew Symmetric Splitting Method. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, Cilt: 7 Sayı: 1, 319–328. https://doi.org/10.35193/bseufbd.670846

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References (7)

  1. Z.Z. Bai, G.H. Golub and M.K. Ng (2003). Hermitian and Skew Hermitian Splitting Methods for Non-Hermitian Positive Definitive Linear Systems, SIAM J. Appl. Math. 24(3), 603-626.
  2. Z.Z. Bai, M. Benzi, F. Chen (2011). On preconditioned MHSS iteration methods for complex symmetric linear systems, Numer. Algorithms, 56, 297-317.
  3. M. Dehghan, A. Shirilord (2019). A generalized modified Hermitian and Skew Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation, Appl. Math. Comput. 348, 632-651.
  4. M. Hajarian (2018). Biconjugate residual algorithm for solving General Sylvester-transpose matrix equations, Filomat, 32:15, 5307-5318.
  5. J.W. Demmel, Applied Numerical Linear Algebra (first edition), Siam, Berkeley (1997).
  6. R.A. Horn, C.R. Johnson, Matrix Analysis (second edition), Cambridge University Press, New York (2012).
  7. B. Zhou, J. Lam, G.R. Duan (2011). Toward solution of matrix equation X = Af(X)B + C, Linear Algebra Appl. 435, 1370–1398.