2005
DOI: 10.1007/s10092-005-0107-z
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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… Show more

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Cited by 86 publications
(57 citation statements)
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“…These structured matrices originate mainly from two distinct application fields: computing generalized eigenvalues (Gohberg et al, 1985;Vandebril et al, 2005Vandebril et al, , 2007, and solving partial differential equations for particule simulation with the fast multipole method (Carrier et al, 1988). This class also arise naturally, as it includes the closure under inversion of the class of banded matrices.…”
Section: Introductionmentioning
confidence: 99%
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“…These structured matrices originate mainly from two distinct application fields: computing generalized eigenvalues (Gohberg et al, 1985;Vandebril et al, 2005Vandebril et al, , 2007, and solving partial differential equations for particule simulation with the fast multipole method (Carrier et al, 1988). This class also arise naturally, as it includes the closure under inversion of the class of banded matrices.…”
Section: Introductionmentioning
confidence: 99%
“…Taking advantage of the low rank properties, mainly two types of structured representations have been developped together with corresponding dedicated algorithms to perform common linear algebra operations: the quasiseparable generators of Vandebril et al (2005Vandebril et al ( , 2007, sometimes referred to as sequentially semiseparable (SSS) and the hierarchically semiseparable representations (HSS) of Chandrasekaran et al (2006); Xia et al (2010). We refer to (Vandebril et al, 2005) and (Vandebril et al, 2007) for a broad bibliographic overview on the topic. Note also the alternative approach of Givens and unitary weights in Delvaux and Van Barel (2007).…”
Section: Introductionmentioning
confidence: 99%
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“…We refer to the paper [78] for a commented bibliography starting from the pioneering papers by Gantmaker and Krein in 1937, and to the recent books [79], [80], [41], [42] with the state of the art in this field. The research activity on rank structured matrices is very intense, there are several international groups which are very active and have produced interesting theoretical and algorithmic advances.…”
Section: Introductionmentioning
confidence: 99%
“…(See [24] for related historical remarks.) More recently, understanding the structure of Inv(V ) has turned out to be central in matrix factorization problems and large scale numerical linear algebra of preconditioning [13], [4].…”
Section: Introductionmentioning
confidence: 99%