Speaker: Federico Poloni
Affiliation: Department of Computer Science, University of Pisa
Time: Thursday, 04/07/2019
Place: Aula Magna, Dipartimento di Matematica
Title: Principal pivot transforms, quasidefinite matrices, and matrix
equations
Principal pivot transforms are maps between matrices that generalize, in
some sense, Schur complementation and inversion. They are a somewhat
counterintuitive but powerful tool that allows one to
reinterpret Gaussian elimination-type algorithms in a different framework.
We will show how they can deal successfully with various kinds of
matrices in a structure-preserving way; this includes (weakly)
quasi-definite matrices, i.e., symmetric matrices with two complementary
diagonal blocks of opposite definiteness, as well as
Hamiltonian/symplectic matrices. We will then present an algorithm to
solve dense algebraic Riccati equations in a factored form, which relies
on these transforms as a basic building block.
