On multiplier sequences

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• 作者：Vladimir Petrov Kostov
• 关键词：Hyperbolic polynomial ; Hyperbolicity domain ; Stratification ; Multiplicity vector ; Finite multiplier sequence
• 刊名：Theoretical Computer Science
• 出版年：2008
• 出版时间：28 February 2008
• 年：2008
• 卷：392
• 期：1-3
• 页码：101-112
• 全文大小：375 K

文摘

In the present paper we consider real polynomials in one real variable of a given degree V1G-4PV2S4B-6&_mathId=mml1&_user=10&_cdi=5674&_rdoc=9&_acct=C000050221&_version=1&_userid=10&md5=c548a37aa8e3c9aaf2e9606159df3b5f"" title=""Click to view the MathML source"">n. Such a polynomial is called hyperbolic if it has only real roots. A finite multiplier sequence of length n+1 (FMS(n+1)) is a tuple (c₀,…,c_n), , such that if , , is a hyperbolic polynomial, then is also such a polynomial. The set of FMS(n+1) coincides with the set of tuples such that is a hyperbolic polynomial with all roots of the same sign. In the paper we prove several geometric properties of the set of FMS(n+1) formulated in terms of its stratification (defined by the multiplicity vectors of the polynomials) and of the Whitney property (the curvilinear distance to be equivalent to the Euclidean one).