On the computation of the elementary divisors and the Smith normal form of homogeneous matrix pencils

Abstract

In this paper we present a numerical algorithm for the computation of the elementary divisors of a given homogeneous matrix pencil based on the new Piecewise Arithmetic Progression Sequence (PAPS) method. This specific method constructs the so-called PAPS diagram from which one can directly determine the elementary divisors of the given pencil. The PAPS approach is then applied for the computation of the Smith normal form of the pencil.