### Subject: Characterization of positive polynomials

Date: **Tue Mar 7 07:15:45 2000**

Posted by **Simon, C.M.Lee**

Grade level: **grad (science)**
School: **City University of Hong Kong**

City: **Hong Kong** State/Province: **Hong Kong**
Country: **China**

Area of science: **Computer Science**

ID: **952434945.Cs**

**Message:**

Dear Professor,
I am very grateful if the following mathematical problem is
solved, and the related web site is found.
Let n be a positive integer and p(x) is a real polynomial of degree
n-1. Find a necessary and sufficient condition for the coefficients
of p(x) such that p(x)>=0 on the closed interval -1<=x<=1. An
equivalent condition is the set of coefficients
{(a_0, a_1, ..., a_{n-1}): p(1), p(-1), p(x_0) >=0 for all
turning points p'(x_0)=0}.
Is there any handy or parametric way of representing those
coefficients?
Thanks a lot
Warmest regards,
Simon

Re: Characterization of positive polynomials

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