Computing Approximate GCD of Univariate Polynomials

被引：5
|
作者：
Khare, S. R. [1 ]
Pillai, H. K. [1 ]
Belur, M. N. [1 ]
机构：
[1] Indian Inst Technol, Dept Elect Engn, Bombay 400076, Maharashtra, India
来源：
18TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION | 2010年
关键词：
Approximate GCD of polynomials; Nullspace of a Polynomial Matrix; SVD; Structured Low Rank Approximation (SLRA); GREATEST COMMON DIVISOR; COMPUTATION; SYLVESTER; MATRIX;
D O I：
10.1109/MED.2010.5547707
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper we discuss the problem of computing the approximate GCD of two univariate polynomials. We construct a linearly structured resultant matrix from given polynomials. We show the equivalence of the full rank property of this resultant matrix and the coprimeness of the polynomials. Further we show that the nearest structured low rank approximation (SLRA) of the resultant matrix gives the approximate GCD of the polynomials. We formulate the problem of computing the nearest SLRA as an optimization problem on a smooth manifold, namely the unit sphere SN-1 in R-N.
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页码：437 / 441
页数：5
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