Rank structured matrix operations
Marc Van Barel, Raf Vandebril, Nicola Mastronardi, Steven Delvaux, Yvette Vanberghen · 2006
Classically, several numerical linear algebra problems are solved by means of tridiagonal (symmetric) and Hessenberg (unsymmetric) matrices. In this talk, it will be shown that a similar role can be played by semiseparable matrices. A matrix is called semiseparable if all submatrices that can be taken out of the lower triangular part (the main diagonal included) have maximum rank one. We will study how several matrix operations can be performed on such semiseparable, as well as more general rank structured matrices in an efficient and accurate way. We will illustrate the algorithms by means of several numerical examples.