Computing Popov and Hermite Forms of Rectangular Polynomial Matrices

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Abstract

We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are known. Here, we present deterministic, fast algorithms for rectangular input matrices. The obtained cost bound for the Popov form matches the previous best known randomized algorithm, while the cost bound for the Hermite form improves on the previous best known ones by a factor which is at least the largest dimension of the input matrix.
Original languageEnglish
Title of host publicationProceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation
Number of pages8
PublisherAssociation for Computing Machinery
Publication date2018
Pages295-302
ISBN (Print)978-1-4503-5550-6
DOIs
Publication statusPublished - 2018
Event2018 ACM International Symposium on Symbolic and Algebraic Computation - New York, United States
Duration: 16 Jul 201819 Jul 2018

Conference

Conference2018 ACM International Symposium on Symbolic and Algebraic Computation
CountryUnited States
CityNew York
Period16/07/201819/07/2018

Keywords

  • Polynomial matrix
  • Reduced form
  • Popov form
  • Hermite form

Cite this

Neiger, V., Rosenkilde, J. S. H., & Solomatov, G. A. (2018). Computing Popov and Hermite Forms of Rectangular Polynomial Matrices. In Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation (pp. 295-302). Association for Computing Machinery. https://doi.org/10.1145/3208976.3208988