广义多项式ax + by = d的解

The 23rd IEEE Conference on Decision and Control Pub Date : 1984-12-01 DOI:10.1109/CDC.1984.272439

S. Barnett

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引用次数: 2

摘要

本文描述了求解方程ax + by = d的一种简单矩阵法，其中已知A和b，并求出x、y和最大公约数d。所有的多项式都是相对于正交多项式的任意给定基来表示的，并且没有幂形式的转换。该程序利用同伴矩阵，一种同伴矩阵的推广，并涉及在容易构造的矩阵上执行的初等行运算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solution of ax + by = d for generalized polynomials

A simple matrix method is described for solving the equation ax + by = d, where a and b are given, and x, y and the greatest common divisor (g.c.d.) d are to be determined. All the polynomials are expressed relative to an arbitrary given basis of orthogonal polynomials, and there are no conversions to power form. The procedure utilizes the comrade matrix, a generalization of the companion matrix, and involves elementary row operations performed on easily constructed matrices.

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The 23rd IEEE Conference on Decision and Control

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