Tajaddini, A., Sheybani, M., Yaghoobi, M. (2019). A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation. Wavelet and Linear Algebra, 5(2), 29-45. doi: 10.22072/wala.2019.93411.1197

Azita Tajaddini; Malihe Sheybani; Mohammad Ali Yaghoobi. "A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation". Wavelet and Linear Algebra, 5, 2, 2019, 29-45. doi: 10.22072/wala.2019.93411.1197

Tajaddini, A., Sheybani, M., Yaghoobi, M. (2019). 'A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation', Wavelet and Linear Algebra, 5(2), pp. 29-45. doi: 10.22072/wala.2019.93411.1197

Tajaddini, A., Sheybani, M., Yaghoobi, M. A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation. Wavelet and Linear Algebra, 2019; 5(2): 29-45. doi: 10.22072/wala.2019.93411.1197

A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation

^{1}Department of Applied Mathematics, Faculty of Mathematics &amp; Computer Sciences, Shahid Bahonar University of Kerman

^{2}Department of Applied Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

^{3}Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

Global Krylov subspace methods are the most ecient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergence and symmetric positive definite splitting of the coecient matrices. Convergence properties of this method are investigated. Finally, the eectiveness of the nested splitting conjugate gradient method is explained by some numerical examples.