Reliable numerical methods for polynomial matrix triangularization

Henrion D.; Sebek M.

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Reliable numerical methods for polynomial matrix triangularization

机译：多项式矩阵三角化的可靠数值方法

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Numerical procedures are proposed for triangularizing polynomial matrices over the field of polynomial fractions and over the ring of polynomials. They are based on two standard polynomial techniques: Sylvester matrices and interpolation. In contrast to other triangularization methods, the algorithms described in this paper only rely on well-worked numerically reliable tools. They can also be used for greatest common divisor extraction, polynomial rank evaluation, or polynomial null-space computation

机译：为在多项式分数域和多项式环上三角化多项式矩阵，提出了数值程序。它们基于两种标准的多项式技术：Sylvester矩阵和插值。与其他三角化方法相比，本文描述的算法仅依赖于工作良好的数值可靠工具。它们还可以用于最大公约数提取，多项式秩评估或多项式零空间计算

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《IEEE Transactions on Automatic Control》 |1999年第3期|p.497-508|共12页
作者
Henrion D.; Sebek M.;
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正文语种 eng
中图分类自动化系统;
关键词
interpolation; numerical analysis; polynomial matrices; Sylvester matrices; interpolation; numerical methods; polynomial fractions; polynomial matrix; polynomial null-space; polynomial rank evaluation; triangularization;

机译：插值;数值分析;多项式矩阵;Sylvester矩阵;插值;数值方法;多项式分数;多项式矩阵;多项式零空间;多项式等级评估;三角化;

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1. Reliable numerical methods for polynomial matrix triangularization [J] . Henrion D., Sebek M. IEEE Transactions on Automatic Control . 1999,第3期

机译：多项式矩阵三角化的可靠数值方法
2. A matrix triangularization algorithm for the polynomial point interpolation method [J] . G.R. Liu, Y.T. Gu Computer Methods in Applied Mechanics and Engineering . 2003,第19期

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7. Reliable Numerical Methods for Polynomial Matrix Triangularization [O] . Didier Henrion, Michael Sebek 1999

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8. On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems [R] . Belcastro, Christine M. 1998

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Reliable numerical methods for polynomial matrix triangularization

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