Proper splittings and reduced solutions of matrix equations

ARIAS, M. LAURA; GONZALEZ, M. CELESTE

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2022 vol. 505

0022-247X

In this article we apply proper splittings of matrices to develop an iterative process to approximate solutions of matrix equations of the form . Moreover, by using the partial order induced by positive semidefinite matrices, we obtain equivalent conditions to the convergence of this process. We also include some speed comparison results of the convergence of this method. In addition, for all matrix T we propose a proper splitting based on the polar decomposition of T.