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

Yıl 2022, Cilt: 5 Sayı: 2, 98 - 105, 01.06.2022

Oguzer Sinan Sefa Baydak Ahmet Duman Kemal Aydın

https://doi.org/10.33401/fujma.996668

Öz

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.

Anahtar Kelimeler

Hurwitz stability IDDM Lyapunov matrix equations Schur stability

Teşekkür

The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

Kaynakça

  • [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.

Yıl 2022, Cilt: 5 Sayı: 2, 98 - 105, 01.06.2022

Oguzer Sinan Sefa Baydak Ahmet Duman Kemal Aydın

https://doi.org/10.33401/fujma.996668

Öz

Kaynakça

  • [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.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Oguzer Sinan 0000-0002-8742-5372

Sefa Baydak 0000-0002-0337-3342

Ahmet Duman 0000-0002-4022-5285

Kemal Aydın 0000-0001-7822-3384

Yayımlanma Tarihi 1 Haziran 2022
Gönderilme Tarihi 20 Eylül 2021
Kabul Tarihi 19 Mart 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA 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, 5(2), 98-105. https://doi.org/10.33401/fujma.996668
AMA Sinan O, Baydak S, Duman A, Aydın K. Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method. FUJMA. Haziran 2022;5(2):98-105. doi:10.33401/fujma.996668
Chicago Sinan, Oguzer, Sefa Baydak, Ahmet Duman, ve Kemal Aydın. “Computation of the Solutions of Lyapunov Matrix Equations With Iterative Decreasing Dimension Method”. Fundamental Journal of Mathematics and Applications 5, sy. 2 (Haziran 2022): 98-105. https://doi.org/10.33401/fujma.996668.
EndNote Sinan O, Baydak S, Duman A, Aydın K (01 Haziran 2022) Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method. Fundamental Journal of Mathematics and Applications 5 2 98–105.
IEEE O. Sinan, S. Baydak, A. Duman, ve K. Aydın, “Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method”, FUJMA, c. 5, sy. 2, ss. 98–105, 2022, doi: 10.33401/fujma.996668.
ISNAD Sinan, Oguzer vd. “Computation of the Solutions of Lyapunov Matrix Equations With Iterative Decreasing Dimension Method”. Fundamental Journal of Mathematics and Applications 5/2 (Haziran 2022), 98-105. https://doi.org/10.33401/fujma.996668.
JAMA Sinan O, Baydak S, Duman A, Aydın K. Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method. FUJMA. 2022;5:98–105.
MLA Sinan, Oguzer vd. “Computation of the Solutions of Lyapunov Matrix Equations With Iterative Decreasing Dimension Method”. Fundamental Journal of Mathematics and Applications, c. 5, sy. 2, 2022, ss. 98-105, doi:10.33401/fujma.996668.
Vancouver Sinan O, Baydak S, Duman A, Aydın K. Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method. FUJMA. 2022;5(2):98-105.
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