Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation

Abstract

By introducing the real inner product, this paper offers an modified conjugate gradient least squares iterative algorithm (MCGLS)for solving the generalized Sylvester-conjugate matrix equation. The properties of this algorithm are discussed and the finite convergence of this algorithm is proven. This new iterative method can obtain the symmetric least squares Frobenius norm solution
within finite iteration steps in the absence of roundoff errors. Finally, two numerical examples are
offered to illustrate the effectiveness of the proposed algorithm.