Genelleştirilmiş Sylvester Transpoz Matris Denkleminin Simetrik – Ters Simetrik Ayrışım Metodu ile Çözümü
Öz
Bu çalışmada Ax=b lineer denklem sisteminin çözümü için Simetrik-Ters Simetrik Ayrışım (SSS) metodu tanıtıldı. Daha sonra
AXB+CXD+EXT F=M
genelleştirilmiş Sylvester Transpoze matris denkleminin çözümü bu metot kullanılarak ortaya konuldu. Son olarak SSS metodunun performansını resmeden sayısal bir örnek verildi.
Anahtar Kelimeler
SSS metodu Genelleştirilmiş Sylvester transpoz matris denklemi Kronecker çarpım Matris normu Spektral yarıçap
Kaynakça
- 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.
- Z.Z. Bai, M. Benzi, F. Chen (2011). On preconditioned MHSS iteration methods for complex symmetric linear systems, Numer. Algorithms, 56, 297-317.
- 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.
- M. Hajarian (2018). Biconjugate residual algorithm for solving General Sylvester-transpose matrix equations, Filomat, 32:15, 5307-5318.
- J.W. Demmel, Applied Numerical Linear Algebra (first edition), Siam, Berkeley (1997).
- R.A. Horn, C.R. Johnson, Matrix Analysis (second edition), Cambridge University Press, New York (2012).
- B. Zhou, J. Lam, G.R. Duan (2011). Toward solution of matrix equation X = Af(X)B + C, Linear Algebra Appl. 435, 1370–1398.
On Solution of Generalized Sylvester Transpose Matrix Equation Using Symmetric – Skew Symmetric Splitting Method
Öz
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+EXT 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.
Anahtar Kelimeler
SSS method Generalized Sylvester transpose matrix equation Kronecker product Matrix norm Spectral radius
Kaynakça
- 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.
- Z.Z. Bai, M. Benzi, F. Chen (2011). On preconditioned MHSS iteration methods for complex symmetric linear systems, Numer. Algorithms, 56, 297-317.
- 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.
- M. Hajarian (2018). Biconjugate residual algorithm for solving General Sylvester-transpose matrix equations, Filomat, 32:15, 5307-5318.
- J.W. Demmel, Applied Numerical Linear Algebra (first edition), Siam, Berkeley (1997).
- R.A. Horn, C.R. Johnson, Matrix Analysis (second edition), Cambridge University Press, New York (2012).
- B. Zhou, J. Lam, G.R. Duan (2011). Toward solution of matrix equation X = Af(X)B + C, Linear Algebra Appl. 435, 1370–1398.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Haziran 2020 |
| Gönderilme Tarihi | 6 Ocak 2020 |
| Kabul Tarihi | 29 Haziran 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 7 Sayı: 1 |