Linear and Nonlinear Matrix Equations

Abstract

Matrix equations have practical applications in many areas such as computational mathematics, biology, electricity, dynamic programming, stochastic filtering, statistics, solid mechanics, and control and system theory. In recent years, a large number of papers have studied several linear and nonlinear matrix equations. This special issue is devoted to publishing the latest and significant results on linear and nonlinear matrix equations on all their aspects. Its goals are to highlight recent advances and developments on themany facets, techniques, and results of linear and nonlinear matrix equations. The topics included in this special issue are iterative solutions of matrix equations, closed-form solutions and solvability of matrix equations, quaternion matrix equations, and perturbation analysis of matrix equations. We received nineteen papers in the interdisciplinary research fields.This special issue includes seven high qualitypeer-reviewed articles. In the following, we briefly review each of the papers that are published. In the paper entitled “Norm-constrained least-squares solutions to the matrix equation AXB = C,” A. Xu and B. Z. Peng propose an iterative method to compute the leastsquares solutions of the matrix equation AXB = C over the norm inequality constraint. In the paper entitled “Iterative solution to a system of matrix equations,” Y. Lin and Q. W. Wang introduce an efficient iterative algorithm to solve the system of linear matrix equations A 1 X 1 B 1 + A 2 X 2 B 2 = E and C 1 X 1 D 1 +