A bibliography on semiseparable matrices*

R. Vandebril, M. Van Barel, G. Golub, N. Mastronardi
2005 Calcolo  
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
more » ... tatisticians 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. Article information • Vandebril, Raf; Van Barel, Marc; Golub, G.; Mastronardi, Nicola. A bibliography on semiseparable matrices, Calcolo, volume 42, issue 3-4, pages 249-270, 2005. • The content of this article is identical to the content of the published paper, but without the final typesetting by the publisher. • Journal's homepage: Abstract Currently there is a growing interest in semiseparable matrices and generalized semiseparable matrices. As it is interesting to know 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 interesting to know is that the 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, as they were sometimes 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 know them nowadays.
doi:10.1007/s10092-005-0107-z fatcat:dj3ema4whveg3l725gofhrpir4