Shifted Global BiCG-Type Methods for Solving the Large Stein Equation X + AXB = C

Abstract

The Stein matrix equation plays an essential role in control and communications theory, linear algebra, image restoration, and so on. In this paper, we propose two shifted variants of global BiCG-type methods to solve the large Stein matrix equation which make full use of the shifted structure of the matrix equation. These modifications will not add more matrix-matrix multiplications and inner products. Finally, numerical examples are given to illustrate the effectiveness of the presented methods.