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A compound matrix algorithm for the computation of the Smith form of a polynomial matrix

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Abstract

In the present paper is presented a numerical method for the exact reduction of a singlevariable polynomial matrix to its Smith form without finding roots and without applying unimodular transformations. Using the notion of compound matrices, the Smith canonical form of a polynomial matrixM(s)∈ℝnxn[s] is calculated directly from its definition, requiring only the construction of all thep-compound matricesC p (M(s)) ofM(s), 1<p≤n. This technique produces a stable and accurate numerical algorithm working satisfactorily for any polynomial matrix of any degree.

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimiopolis, GR-157 84, Athens, Greece

    M. Mitrouli & G. Kalogeropoulos

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  1. M. Mitrouli
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  2. G. Kalogeropoulos
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Communicated by W. M. Coughran, Jr.

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Mitrouli, M., Kalogeropoulos, G. A compound matrix algorithm for the computation of the Smith form of a polynomial matrix. Numer Algor 7, 145–159 (1994). https://doi.org/10.1007/BF02140679

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  • DOI: https://doi.org/10.1007/BF02140679

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