On real factors of real interval polynomials
On real factors of real interval polynomials
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关于实数区间多项式的实因式
DOI：
10.1145/1277548.1277593
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Hiroshi Sekigawa
中科院分区：
文献类型：
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作者：
Hiroshi Sekigawa
对于实多元区间多项式P和实多元多项式F，给出了判定P中是否存在P可被F整除的多项式的严格方法。当P是单变量时，有一个众所周知的准则来判断P中是否存在多项式(χ)，使得对于给定的实数α，P(α)=0。由于p(α)=0当且仅当p(χ)可被χ--α整除，我们的结果推广到多元多项式和高次因子。
For a real multivariate interval polynomial <i>P</i> and a real multivariate polynomial <i>f</i>, we provide a rigorous method for deciding whether there exists a polynomial <i>p</i> in <i>P</i> such that <i>p</i> is divisible by <i>f</i>. When <i>P</i> is univariate, there is a well-known criterion for whether there exists a polynomial <i>p</i>(χ)in <i>P</i> such that <i>p</i>(α)=0 for a given real number α. Since <i>p</i>(α)=0 if and only if <i>p</i>(χ) is divisible by χ--α, our result is a generalization of the criterion to multivariate polynomials and higher degree factors.