A new algorithm for the solution of a polynomial matrix Diophantine equation

Tzekis PA

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A new algorithm for the solution of a polynomial matrix Diophantine equation

机译：多项式矩阵丢番图方程求解的新算法

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The main contribution of this work is to provide a new algorithm for the general solution of a polynomial matrix Diophantine equation. The theory is implemented via illustrative examples. (C) 2007 Elsevier Inc. All rights reserved.

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《Applied mathematics and computation》 |2007年第2期|共13页
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Tzekis PA;
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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Diophantine equations; polynomial methods; NONLINEAR-SYSTEMS; DESIGN;

机译：Diophantine方程;多项式方法;非线性系统;设计;

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1. A new algorithm for the solution of a polynomial matrix Diophantine equation [J] . Tzekis PA Applied mathematics and computation . 2007,第2期

机译：多项式矩阵丢番图方程求解的新算法
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4. Unified Parametrization for the Solutions to the Polynomial Diophantine Matrix Equation and the Generalized Sylvester Matrix Equation [C] . The 7th World Congress on Intelligent Control and Automation(WCICA'08)(第七届智能控制与自动化世界大会)论文集 . 2008

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5. Lossless Data Compression by Representing Data as a Solution to the Diophantine Equations [D] . Grewal, Karandeep Singh. 2021

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6. An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations [O] . Zhongli Zhou, Guangxin Huang 2013

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7. The performance of available methods for computing the polynomial coefficients of the quadratic function approximation is evaluated. By comparing the numerical results to those obtained by symbolic methods, for a variety of functions, the direct solution of the matrix equation and a variety of recursive algorithms are all shown to be numerically unstable. AMS classification [O] . Balakrishnan Easwaran, McInnes A.W. 1991

机译：评估了用于计算二次函数逼近的多项式系数的可用方法的性能。通过将数值结果与通过符号方法获得的数值结果进行比较，对于多种函数，矩阵方程的直接解法和多种递归算法均显示出数值上的不稳定。 AMS分类

A new algorithm for the solution of a polynomial matrix Diophantine equation

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