Zobrazeno 1 - 10
of 52 447
pro vyhledávání: '"sums of squares"'
In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency matrix of a graph by an expression that behaves monotonically in terms of
Externí odkaz:
http://arxiv.org/abs/2411.08184
Autor:
Laurent, Monique, Slot, Lucas
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex) optimization
Externí odkaz:
http://arxiv.org/abs/2408.04417
In this paper, we derive a general formula to express the product of three theta functions as a linear combination of other products of three theta functions. Moreover, we use the main formula to deduce a general formula for the product of two theta
Externí odkaz:
http://arxiv.org/abs/2410.13555
Autor:
Mukasa, Hirai, Tsukuda, Koji
General ridge estimators are typical linear estimators in a general linear model. The class of them include some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the weighted le
Externí odkaz:
http://arxiv.org/abs/2405.20023
We initiate a systematic study of nonnegative polynomials $P$ such that $P^k$ is not a sum of squares for any odd $k\geq 1$, calling such $P$ \emph{stubborn}. We develop a new invariant of a real isolated zero of a nonnegative polynomial in the plane
Externí odkaz:
http://arxiv.org/abs/2407.21779
Autor:
Kowalczyk, Tomasz
Let $C$ be an irreducible nonsingular curve over a formally real field $K$ and let $f$ be a regular function which is a sum of squares in the ring of regular functions of the surface $C \times \mathbb{A}_K$. We show that the (sum of squares) length o
Externí odkaz:
http://arxiv.org/abs/2407.20378