Structured Matrices

The expression structured matrices appeared for the first time in a conference title in 1995, specifically in the session “Algorithms for Structured Matrices”, organized within the SPIE conference, held in San Diego (USA) [1, Session 6] and in the “Minisymposium on Structured Matrices” within the ILAS conference, held in Atlanta (USA) [2]. These first experiences led to the organization, in 1996, of the first two conferences specifically devoted to structured matrices: “International Workshop on Numerical Methods for Structured Matrices in Filtering and Control”, held in Santa Barbara (USA) [3] and “Toeplitz Matrices: Structures, Algorithms and Applications” held in Cortona (Italy) [4]. The organization of specific conferences on structured matrices has given the opportunity to meet together researchers working on theoretical and computational properties of structured matrices, and researchers working on applications. This exchange of experts from different fields has led to strong benefits to researches interested in structured matrices. This anniversary gives the opportunity to reflect on the state-of-art in the research involving matrix structures in the last 15 years. The aim of this talk is to survey some key results achieved along different directions, paying special attention to the significant contribution of the italian research group on structured numerical linear algebra, having its main site in Pisa. In particular, the four editions of the Cortona Workshop offer a privileged point of view in this context. Some pointers to future research perspectives will be also given.