research-article

Further results on the factorization and equivalence for multivariate polynomial matrices

Authors:

Fanghui XiaoAuthors Info & Claims

ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation

Pages 328 - 335

https://doi.org/10.1145/3373207.3404020

Published: 27 July 2020 Publication History

Abstract

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present a new criterion for the existence of matrix factorizations for a class of multivariate polynomial matrices, and prove that these matrix factorizations are unique. Based on this new criterion and the constructive proof process, we give an algorithm to compute a matrix factorization of a multivariate polynomial matrix. After that, we put forward a sufficient and necessary condition for the equivalence of square polynomial matrices: a square polynomial matrix is equivalent to a diagonal triangle if it satisfies the condition. An illustrative example is given to show the effectiveness of the matrix equivalence theorem.

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Cited By

Guan JLiu JZheng LWu TLiu J(2024)New Results on Equivalence of Multivariate Polynomial MatricesJournal of Systems Science and Complexity10.1007/s11424-024-2288-zOnline publication date: 14-Mar-2024
https://doi.org/10.1007/s11424-024-2288-z
Lu DWang DXiao FZheng X(2023)Equivalence and reduction of bivariate polynomial matrices to their Smith formsJournal of Symbolic Computation10.1016/j.jsc.2023.01.001Online publication date: Jan-2023
https://doi.org/10.1016/j.jsc.2023.01.001
Zheng XLu DWang DXiao F(2023)New Results on the Equivalence of Bivariate Polynomial MatricesJournal of Systems Science and Complexity10.1007/s11424-023-1304-z36:1(77-95)Online publication date: 1-Mar-2023
https://doi.org/10.1007/s11424-023-1304-z
Show More Cited By

Index Terms

Further results on the factorization and equivalence for multivariate polynomial matrices
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation

July 2020

480 pages

ISBN:9781450371001

DOI:10.1145/3373207

General Chairs:
Ioannis Z. Emiris
National and Kapodistrian University of Athens, ATHENA Research and Innovation Center, Greece
,
Lihong Zhi
Academia Sinica, China
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Publications Chair:
Angelos Mantzaflaris
Inria, France

Copyright © 2020 ACM.

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Published: 27 July 2020

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Chinese Academy of Sciences Key Project

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ISSAC '20

ISSAC '20: International Symposium on Symbolic and Algebraic Computation

July 20 - 23, 2020

Kalamata, Greece

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ISSAC '20 Paper Acceptance Rate 58 of 102 submissions, 57%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Guan JLiu JZheng LWu TLiu J(2024)New Results on Equivalence of Multivariate Polynomial MatricesJournal of Systems Science and Complexity10.1007/s11424-024-2288-zOnline publication date: 14-Mar-2024
https://doi.org/10.1007/s11424-024-2288-z
Lu DWang DXiao FZheng X(2023)Equivalence and reduction of bivariate polynomial matrices to their Smith formsJournal of Symbolic Computation10.1016/j.jsc.2023.01.001Online publication date: Jan-2023
https://doi.org/10.1016/j.jsc.2023.01.001
Zheng XLu DWang DXiao F(2023)New Results on the Equivalence of Bivariate Polynomial MatricesJournal of Systems Science and Complexity10.1007/s11424-023-1304-z36:1(77-95)Online publication date: 1-Mar-2023
https://doi.org/10.1007/s11424-023-1304-z
Lu DWang DXiao F(2022)New Remarks on the Factorization and Equivalence Problems for a Class of Multivariate Polynomial MatricesJournal of Symbolic Computation10.1016/j.jsc.2022.07.005Online publication date: Aug-2022
https://doi.org/10.1016/j.jsc.2022.07.005
Liu JWu TLi D(2022)Smith Form of Triangular Multivariate Polynomial MatrixJournal of Systems Science and Complexity10.1007/s11424-022-1289-z36:1(151-164)Online publication date: 13-Sep-2022
https://doi.org/10.1007/s11424-022-1289-z

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