Sparse linearizations and (sparse) structured ell-ifications

Data Seminario: 
18-Mar-2019
Ora Inizio: 
14:00
Ora Fine: 
15:00
Carla Hernando
Universidad Carlos III, Madrid

The talk is divided in two main parts. The first one is focused on
(generalized) companion pencils, which are strong linearizations and
they present a template involving no arithmetic operations at all. In
addition, we are mainly interested in sparse (generalized) companion
pencils and then, we determine the smallest number of nonzero entries of
a particular class of companion pencils. In the case of generalized
companion pencils, we should impose natural conditions on its entries.
In the second one, a family of structured block Kronecker ell-ifications
will be introduced. This family has the particular structure of a
strong block minimal bases polynomial, introduced in [1]. Furthermore,
we have introduced two new subfamilies of structured block Kronecker
ell-ifications where not only there is no duplication of the
coefficients of the polynomial, but also the degree-ell polynomial is
sparse.

This is joint work with Fernando de Terán (UC3M, Spain), my thesis
director.

[1] F.M.Dopico, J.Pérez, P.Van Dooren. Block minimal bases
ell-ifications of matrix polynomials. Linear Algebra Appl., 562 (2019),
163-204