Exact computations with quasiseparable matrices
Abstract
Quasi-separable matrices are a class of rank-structured matrices
widely used in numerical linear algebra and of growing interest
in computer algebra, with applications in e.g. the linearization of
polynomial matrices. Various representation formats exist for these
matrices that have rarely been compared.
We show how the most central formats SSS and HSS can be
adapted to symbolic computation, where the exact rank replaces
threshold based numerical ranks. We clarify their links and compare
them with the Bruhat format. To this end, we state their space and
time cost estimates based on fast matrix multiplication, and compare
them, with their leading constants. The comparison is supported
by software experiments.
We make further progresses for the Bruhat format, for which we
give a generation algorithm, following a Crout elimination scheme,
which specializes into fast algorithms for the construction from a
sparse matrix or from the sum of Bruhat representations.
Origin : Files produced by the author(s)