On the positivity and convexity of polynomials
Authors: Zheng, J.J., Chen, X.Q. and Zhang, J.J.
Journal: Ruan Jian Xue Bao/Journal of Software
Volume: 13
Issue: 4
Pages: 510-517
ISSN: 1000-9825
Abstract: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. A practical algorithm to express this condition in terms of the coefficients of the polynomials is also given.
Source: Scopus
On the positivity and convexity of polynomials
Authors: Zheng, J.J., Chen, X.-Q. and Zhang, J.J.
Journal: Journal of Software
Volume: 13
Pages: 510-517
ISSN: 1796-217X
Abstract: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.
http://www.jos.org.cn/1000-9825/13/510.pdf
Source: Manual
Preferred by: Jian Jun Zhang