On computing root polynomials and minimal bases of matrix pencils

We revisit the notion of root polynomials, thoroughly studied in (Dopico and Noferini, 2020 [9]) for general polynomial matrices, show how they can efficiently be computed case a matrix pencil λE+A. The method we propose makes extensive use staircase algorithm, which is known to compute left right minimal indices Kronecker structure pencil. In addition, here that applied expansion (λ−λ0)E+(A−λ0E), constructs block triangular from basis maximal set polynomials at eigenvalue λ0, an efficient manner.