An efficient numerical method for computation of the number of complex zeros of real polynomials inside the open unit disk

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• 作者：Muhammad Mujtaba Shaikh^a ; ^{mujtaba.shaikh@faculty.muet.edu.pk" class="auth_mail" title="E-mail the corresponding author} ; Karem Boubaker^b
• 关键词：Real polynomials ; Complex zeros ; Sturm sequences ; Boubaker polynomials
• 刊名：Journal of the Association of Arab Universities for Basic and Applied Sciences
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：21
• 期：Complete
• 页码：86-91
• 全文大小：572 K

文摘

In this paper, a simple and efficient numerical method is proposed for computing the number of complex zeros of a real polynomial lying inside the unit disk. The proposed protocol uses the Boubaker polynomial expansion scheme (BPES) to build sequence of polynomials based on the concept of Sturm sequences. The method is used in a direct way without using any restrictions in reference to other existing methods. The protocol is applied to some example polynomials of different orders and utility of the algorithm is noticed.