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An extended version of Schur-Cohn-Fujiwara theorem in stability theory
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作者 Yongjian HU Xuzhou ZHAN Gongning CHEN 《Frontiers of Mathematics in China》 SCIE CSCD 2015年第5期1113-1122,共10页
This paper is concerned with root localization of a complex polynomial with respect to the unit circle in the more general case. The classical Schur-Cohn-Fujiwara theorem converts the inertia problem of a polynomial t... This paper is concerned with root localization of a complex polynomial with respect to the unit circle in the more general case. The classical Schur-Cohn-Fujiwara theorem converts the inertia problem of a polynomial to that of an appropriate Hermitian matrix under the condition that the associated Bezout matrix is nonsingular. To complete it, we discuss an extended version of the Schur-Cohn-Fujiwara theorem to the singular case of that Bezout matrix. Our method is mainly based on a perturbation technique for a Bezout matrix. As an application of these results and methods, we further obtain an explicit formula for the number of roots of a polynomial located on the upper half part of the unit circle as well. 展开更多
关键词 Inertia of polynomial inertia of matrix Bezout matrix schur-cohn-fujiwara theorem Schur-Cohn matrix
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