二維離散赫維茨多項式的復系數(shù)列表檢驗法
COMPLEX COEFFICIENTS TABLE TEST FOR TWO-DIMENSIONAL DISCRETE HURWITZ POLYNOMIALS
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摘要: 本文提出了新的二維離散赫維茨(Hurwitz)多項式的檢驗定理。與現(xiàn)有的二維離散赫維茨多項式的代數(shù)檢驗法不同,本文方法是直接對復變量系數(shù)列表,然后利用我們提出的檢驗定理進行零點存在性檢驗,不需在整個x|-1,1]的實數(shù)域進行逐點檢驗,并且無有理多項式出現(xiàn)。因而檢驗過程大為簡化,計算量大為減少,只須進行有限次運算,即可確定其是否是二維離散赫維茨多項式。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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