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TW 400
Steven Delvaux, Marc Van Barel
Rank structures preserved by the QR-algorithm: the singular case
Abstract
In an earlier paper we introduced the classes of polynomial
and rank structures, both of them preserved by applying a (shifted)
QR-step on a matrix A.
In the present paper we will further investigate the case of rank
structures. We
will show that even if A is a singular matrix, a new QR-iterate can be
constructed
having the same rank structure as the matrix A itself.
To this end we will introduce the concepts of effectively eliminating
QR-decompositions
and sparse Givens pattern, both of them being concepts of independent
interest.
