二维离散赫维茨多项式的复系数列表检验法
COMPLEX COEFFICIENTS TABLE TEST FOR TWO-DIMENSIONAL DISCRETE HURWITZ POLYNOMIALS
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摘要: 本文提出了新的二维离散赫维茨(Hurwitz)多项式的检验定理。与现有的二维离散赫维茨多项式的代数检验法不同,本文方法是直接对复变量系数列表,然后利用我们提出的检验定理进行零点存在性检验,不需在整个x|-1,1]的实数域进行逐点检验,并且无有理多项式出现。因而检验过程大为简化,计算量大为减少,只须进行有限次运算,即可确定其是否是二维离散赫维茨多项式。Abstract: The test theorem of 2-D discrete Hurwitz polynomials is proposed. Different from the algebraic methods for the polynomials, the approach of this paper is to list table for complex variable coefficients directly, then to test zero existence for the polynomials with the theorem of this paper. The test proceedure is greatly simplified, and reduces the computations, for it need not to test all x in real domain [-1, 1] point by point and will not meet the rational polynomials. To determine whether they are 2-D discrete Hurwitz polynomialsneeds only finite computations.
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