ON THE COMPUTATION OF THE MINIMAL POLYNOMIAL OF A POLYNOMIAL MATRIX

Nicholas P. KARAMPETAKIS; Panagiotis TZEKIS

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ON THE COMPUTATION OF THE MINIMAL POLYNOMIAL OF A POLYNOMIAL MATRIX

机译：关于多项式矩阵的最小多项式的计算

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摘要

The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples.

机译：这项工作的主要贡献是提供了两种算法来计算单变量多项式矩阵的最小多项式。第一种算法基于线性矩阵方程的解，而第二种算法则采用DFT技术。整个理论通过实例进行说明。

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来源
《International Journal of Applied Mathematics and Computer Science》 |2005年第3期|p.339-349|共11页
作者
Nicholas P. KARAMPETAKIS; Panagiotis TZEKIS;
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作者单位

Department of Mathematics, Aristotle University of Thessaloniki Thessaloniki 54006, Greece;

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原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;
关键词
minimal polynomial; discrete Fourier transform; polynomial matrix; linear matrix equations;

机译：最小多项式离散傅里叶变换多项式矩阵线性矩阵方程;

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1. Solutions to linear matrix ordinary differential equations via minimal, regular, and excessive space extension based universalization Perturbative matrix splines, convergence and error estimate issues for polynomial coefficients in the homogeneous case [J] . Sevda Üsküplü Altınbaşak, Metin Demiralp Journal of Mathematical Chemistry . 2010,第2期

机译：通过基于最小，正则和过度空间扩展的泛化来求解线性矩阵常微分方程组摄动矩阵样条，齐次情形下多项式系数的收敛性和误差估计问题
2. Solutions to linear matrix ordinary differential equations via minimal, regular, and excessive space extension based universalization Convergence and error estimates for truncation approximants in the homogeneous case with premultiplying polynomial coefficient matrix [J] . Sevda Üsküplü Altınbaşak, Metin Demiralp Journal of Mathematical Chemistry . 2010,第2期

机译：线性矩阵常微分方程的解，基于最小，正则和过度空间扩展的泛化对齐次情况下截断近似值的收敛和误差估计，并预先乘以多项式系数矩阵
3. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length: The General Purpose Analog Computer and Computable Analysis Are Two Efficiently Equivalent Models of Computations [J] . Olivier Bournez, Daniel S. Gra{c{c}}a, Amaury Pouly LIPIcs : Leibniz International Proceedings in Informatics . 2016,第2期

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4. On the computation of the minimal polynomial of a two-variable polynomial matrix [C] . Tzekis, P., Karampetakis, . 2005

机译：关于二变量多项式矩阵的最小多项式的计算
5. CLASSIFICATION OF ALL THE MINIMAL BILINEAR ALGORITHMS FOR COMPUTING THE COEFFICIENTS OF TWO POLYNOMIALS MODULO A POLYNOMIAL [D] . AVERBUCH, AMIR. 1984

机译：所有最小双线性算法的分类，用于计算两种多项式模数的系数多项式
6. A WSN Layer-Cluster Key Management Scheme Based on Quadratic Polynomial and Lagrange Interpolation Polynomial [O] . Xiaogang Wang, Zhongfan Yang, Zhiqiang Feng, 2020

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7. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length: The General Purpose Analog Computer and Computable Analysis Are Two Efficiently Equivalent Models of Computations [O] . Bournez Olivier, Graça Daniel S., Pouly Amaury 2016

机译：多项式时间对应于多项式长项的多项式常微分方程的解：通用模拟计算机和可计算分析是两个有效等效的计算模型
8. A Computer Method for Determining the Minimal Polynomial of a Matrix [R] . Latshaw, R. J. 1965

机译：一种确定矩阵最小多项式的计算机方法

ON THE COMPUTATION OF THE MINIMAL POLYNOMIAL OF A POLYNOMIAL MATRIX

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