Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation29453490710.22072/wala.2019.93411.1197ENMaliheSheybaniDepartment of Applied Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranAzitaTajaddiniDepartment of Applied Mathematics, Faculty of Mathematics &amp; Computer Sciences, Shahid Bahonar University of KermanMohammad AliYaghoobiDepartment of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20180910Global Krylov subspace methods are the mostÂ efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergence and symmetric positive definite splitting of the coefficient matrices. Convergence properties of this method are investigated. Finally, the effectiveness of the nested splitting conjugate gradient method is explained by some numerical examples.https://wala.vru.ac.ir/article_34907_bfd916a717266b2a7855f332a24eff29.pdf