Large-scale matrix equations of special type

SUMMARY This issue contains papers dealing with a variety of linear and nonlinear matrix equations arising in systems and control theory, model reduction, and in various other areas of applied mathematics, economics, engineering, and the sciences. Special emphasis is given to the numerical treatment of large-scale problems. This special issue of Numerical Linear Algebra with Applications is devoted to Large-Scale Matrix Equations of Special Type. The term " matrix equations " is generally used for situations where the solution of a mathematical equation is given as a matrix (as opposed to a single vector). with unknown X ∈ F m×p is a simple linear matrix equation. Such equations are not the topic of this issue as (1) can be solved by usual methods for linear systems of equations or linear least-squares problems, maybe with some exploitation of the fact that (1) represents p systems of linear equations (or least-squares problems) sharing the same coefficient matrix A. Thus, (1) does not pose any extra challenge compared to standard linear systems of equations. The term " special type " in the title of this special issue reflects the fact that the contained papers deal with matrix equations having certain structures arising in diverse applications.