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+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.

Anahtar Kelimeler

• SSS metodu,Genelleştirilmiş Sylvester transpoz matris denklemi,Kronecker çarpım,Matris normu,Spektral yarıçap

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+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.

Anahtar Kelimeler

• SSS method,Generalized Sylvester transpose matrix equation,Kronecker product,Matrix norm,Spectral radius

Kaynakça

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.