On the positivity and convexity of polynomials

This source preferred by Jian Jun Zhang

Authors: Zheng, J.J., Chen, X.-Q. and Zhang, J.J.

http://www.jos.org.cn/1000-9825/13/510.pdf

Journal: Journal of Software

Volume: 13

Pages: 510-517

ISSN: 1796-217X

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.

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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

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.

The data on this page was last updated at 05:26 on October 22, 2020.