Name
Abstract | ||
|---|---|---|
A multivariate polynomial F(x1,x2,...,xn) is said to be absolutely positive from a real number B if F and all its partial derivatives are non-negative for x1,x2,...,xn ≥ B. One of the well known bounds on absolute positiveness in the literature is due to Hong. His bound is dependent on the first maximum of a certain sequence of radicals defined using the absolute value of the coefficients of the polynomial. In the univariate setting, a bound due to Lagrange considers the first and the second maximum in the same radical sequence and is shown by Collins to be better than Hong's bound. In the 1930's, Westerfield had proposed a bound that consides every value in the same radical sequence and improves on Lagrange's bound. In this paper, we provide a generalization of Westerfield's bound to the multivariate setting. As a specialization of this bound, we also derive a generalization of Lagrange's bound, which is a strict improvement upon Hong's bound. Finally, we give an algorithm to compute this improved bound. The running time of this algorithm matches the running time of the best known algorithm to compute Hong's bound. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1145/3087604.3087631 | Journal of Symbolic Computation |
Keywords | Field | DocType |
Absolute positiveness, Root bounds, Range trees | Discrete mathematics,Chapman–Robbins bound,Combinatorics,Polynomial,Absolute value,Multivariate statistics,Upper and lower bounds,Partial derivative,Univariate,Real number,Mathematics | Conference |
Citations | PageRank | References |
0 | 0.34 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Swaroop N. Prabhakar | 1 | 0 | 0.34 |
| Vikram Sharma | 2 | 229 | 20.35 |