Unilateral quadratic matrix equations

Abstract

In this chapter, we introduce the unilateral quadratic equations (2) and present several known results on the properties of their solutions and on numerical algorithms, taken mainly from [31]. Moreover, we describe several attempts to generalize the logarithmic reduction algorithm to a generic quadratic vector equation in the framework of Chapter 2, that lead to an unexpected connection with Newton’s algorithm. While the original results contained in this chapter are modest, most of the background material exposed here is needed later in Chapter 6.