%0 Journal Article
%T On the Positivity and Convexity of Polynomials<br>多项式的正性和凸性
%A ZHENG Jin-jin
%A CHEN Xiao-qun
%A ZHANG Jian-jun
%A <br>郑津津
%A 陈效群
%A 张建军
%J 软件学报
%D 2002
%I 
%X The convexity of curves and surfaces is an important property in the field of Computer Aided Geometric Design (CAGD). This paper tries to tackle the positive and convex problem of polynomials. Convexity can be solved by positivity. An algorithm for the positivity of polynomials is developed by extending the classic Sturm theorem. Hence, a necessary and sufficient condition for the positivity of polynomials of arbitrary degree is presented in this paper. A practical algorithm to express this condition in terms of the coefficients of the polynomials is also given.
%K standard sequence
%K greatest common divisor
%K positivity
%K convexity
%K Bernstein-Polynomials<br>标准序列
%K 最大公除数
%K 正性
%K 凸性
%K Bernstein-多项式
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=7735F413D429542E610B3D6AC0D5EC59&aid=1F914A53A6045F13&yid=C3ACC247184A22C1&vid=FC0714F8D2EB605D&iid=E158A972A605785F&sid=25467A5A28500A25&eid=5A751AE9FA58A3FB&journal_id=1000-9825&journal_name=软件学报&referenced_num=0&reference_num=12