A bibliography on semiseparable matrices*

Abstract

Currently there is a growing interest in semiseparable matrices and generalized semiseparable matrices. To gain an appreciation of the historical evolution of this concept, we present in this paper an extensive list of publications related to the field of semiseparable matrices. It is interesting to see that semiseparable matrices were investigated in different fields, e.g., integral equations, statistics, vibrational analysis, independently of each other. Also notable is the fact that leading statisticians at that time used semiseparable matrices without knowing their inverses to be tridiagonal. During this historical evolution the definition of semiseparable matrices has always been a difficult point leading to misunderstandings; sometimes they were defined as the inverses of irreducible tridiagonal matrices leading to generator representable matrices, while in other cases they were defined as matrices having low rank blocks below the diagonal.

In this overview we present a list of interesting results which contributed to the evolution of the concept of semiseparable matrices as we now know them.