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Testing Positiveness of Polynomials

✍ Scribed by Hoon Hong; Dalibor Jakuš

Book ID
110231013
Publisher
Springer Netherlands
Year
1998
Tongue
English
Weight
156 KB
Volume
21
Category
Article
ISSN
0168-7433

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A multivariate polynomial P (x 1 , . . . , xn) with real coefficients is said to be absolutely positive from a real number B iff it and all of its non-zero partial derivatives of every order are positive for x 1 , . . . , xn ≥ B. We call such B a bound for the absolute positiveness of P . This paper

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Let S = N" be a finite set (cq ..... %) of exponents. We construct explicitly a testing set Ts , N" with k elements t~ ..... tk (namely t~ = (2 ~l ..... 2~I')), such that if , a=X~e~[x, ..... x,.], then there exists i (1 \_< i < k) such that P(q) ~ O.

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