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To make clear geometrical structure of an arbitrarily given pencil, it is crucial to understand Kronecker structure of the pencil. For this purpose, GUPTRI is the only practical numerical algorithm at present. However, although GUPTRI determines the Kronecker canonical form (KCF), it does not give any direct information on Kronecker bases (KB). In this paper, we propose a numerical algorithm which gives a full of information on Kronecker structure including KB as well as KCF. The main ingredient of the algorithm is singular value decompositions, which guarantee the backward stability of the algorithm.

Algorithm for computing Kronecker basis