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Dergiler / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 5 Issue: 2

Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method

Oguzer Sinan(Necmettin Erbakan University)0000-0002-8742-5372
Sefa Baydak0000-0002-0337-3342
Ahmet Duman(NECMETTIN ERBAKAN UNIVERSITY, FACULTY OF SCIENCE)0000-0002-4022-5285
Kemal Aydın(SELCUK UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICS)0000-0001-7822-3384
Sayfa
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Yayın Tarihi
2022-06-01
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Computations have been done with Maple procedures that run the constituted algorithms.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The existence of a solution of continuous and discrete-time Lyapunov matrix equations was studied.
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Temel Bulgular & Veri:The iterative decreasing dimension method (IDDM) was implemented for solving the generated matrix-vector equation.
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Sonuç & Katkı:Computations have been done with Maple procedures that run the constituted algorithms.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hurwitz stability · IDDM · Lyapunov matrix equations

Abstract

The existence of a solution of continuous and discrete-time Lyapunov matrix equations was studied. Both Lyapunov matrix equations are transformed into a matrix-vector equation and the solution of the obtained new system was examined. The iterative decreasing dimension method (IDDM) was implemented for solving the generated matrix-vector equation. Computations have been done with Maple procedures that run the constituted algorithms.

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Bu Makaleye Atıf Yap

Sinan, O., Baydak, S., Duman, A., Aydın, K. (2022). Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method. Fundamental Journal of Mathematics and Applications, Volume: 5 Issue: 2. https://doi.org/10.33401/fujma.996668

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Kaynakça (7)

  1. O. Akın, H. Bulgak, Linear Difference Equations and Stability Theory [in Turkish], Selc¸uk University, Research Center of Applied Mathematics, Konya, 1998.
  2. H. Bulgak, Pseudo Eigenvalues, Spectral Portrait of a Matrix and Their Connections with Different Criteria of Stability, In: Error control in Adaptivity in Scientific Computing, H. Bulgak, C. Zenger (editors), NATO Science Series, Kluwer Academic Publishers, 1999, (pp. 95-124).
  3. G. Alexander, Kronecker Products and Matrix Calculus with Applications, John Wiley & Sons, N.Y, 1981.
  4. G. H. Golub C. F. VanLoan, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 2013.
  5. K. Aydın, G. C. Kızılkan, A. O. C¸ ıbıkdiken, Generalized iterative decreasing method, European J. Pure Appl. Math., 3(5)(2010), 819-830.
  6. T. Keskin, K. Aydın, Iterative decreasing dimension algorithm, Comput. Math. Appl., 53(1)(2007), 1153-1158.
  7. H. Vang, J. Jiang, Solution of the system of linear algebraic equations by decreasing dimension, Appl. Math. Comput., 109(1)(2000), 51-57.