ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

Contributed talks on Structured Matrices

Tue 14:00–14:30, Room AV 02.17, Chair: Iwona Wrobel
Parameterized condition numbers for quasiseparable matrices
Kenet J. Pom├ęs (Universidad Carlos III de Madrid)
Joint work with Froilán M. Dopico

Recently, we derived condition numbers for the solution of quasiseparable linear systems with respect to relative perturbations of the parameters in the quasiseparable and in the Givens-vector representations of the system matrix, and for the simple eigenvalues of a quasiseparable matrix also with respect to relative perturbations of the parameters in the quasiseparable and in the Givens-vector representations. In the $\{1,1\}$-case, we obtained similar properties and numerical results for both representations, and we proved that these structured condition numbers may be much smaller than the respective unstructured ones. We extend our approach to the more general case of the $\{n_L,n_U\}$-quasiseparable matrices and present some new results for the structured eigenvalue condition numbers in the general quasiseparable representation and in the Givens-weight representation.