Algebraic reduction methods and their applications to matrix continued fractions

Abstract

A collection of matrices is not always reducible, but it is beneficial for further analysis if it is. Some criteria for the algebraic reducibility have been considered in literature and, indeed, in some cases we are able to compute the reduced forms explicitly. We will review these methods in this paper. As their applications, we will consider the reductions (simplifications) of matrix continued fractions and discuss the convergence problems.