On the solution of generalized Sylvester Transpose matrix equation using symmetric and skew symmetric splitting method

In the first chapter, there are some information about the content and subject of the study. In addition, the historical development of matrices and some studies related to the system of linear equations Ax=b and different matrix equations were mentioned. In the second chapter, it is given some conceps and results that are available in the literature and will be used throughout the study. In Chapter 3, the Biconjugate Residual Algorithm (BCR) is remended related to finding the solution of the coupled general Sylvester transpose matrix equations. In Chapter 4, It is reminded the Hermitian and Skew Hermitian splitting (HSS) method to solve the system of linear equations Ax=b. In Chapter 5, Symmetric and skew symmetric splitting method (SSS) to solve the system of linear equation Ax=b has been introduced. Moreover, it has been established how to solve the generalized Sylvester transpose matrix equation using the SSS method and is given algorithm of this method. Lastly, numerical examples have been given to demonstrate the effectiveness of the SSS method's algorithm. Keywords: SSS method, Sylvester Transpose the matrix equation, Kronecker product, Matrix Norms, Spectral Radius