Fetching the paper…
Reading the bibliography…
Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing.
Idealtheorie in Ringen ohne Endlichkeitsbedingung
Wolfgang Krull. 1929 · 1929
Earlier work this paper cites.
An inequality for the discriminant of a polynomial
Kurt Mahler. 1964 · 1964
Earlier work this paper cites.
On floating point errors in Cholesky
Z Bai, J Demmel, and A McKenney. 1989 · 1989
Earlier work this paper cites.
Geometric Algorithms and Combinatorial Optimization (second corrected edition ed.). Algorithms and Combinatorics, Vol. 2
Martin Grötschel, László Lovász, and Alexander Schrijver. 1993 · 1993
Earlier work this paper cites.
Uniform denominators in Hilbert’s seventeenth problem
Bruce Reznick. 1995 · 1995
Earlier work this paper cites.
On the complexity of semidefinite programs
Lorant Porkolab and Leonid Khachiyan. 1997 · 1997
Earlier work this paper cites.
Algorithmische beweise für nichtnegativ-und positivstellensätze
Markus Schweighofer. 1999 · 1999
Earlier work this paper cites.
The MOSEK interior point optimizer for linear programming: an implementation of the homogeneous algorithm
Erling D Andersen and Knud D Andersen. 2000 · 2000
Earlier work this paper cites.
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
Pablo A Parrilo. 2000 · 2000
Earlier work this paper cites.
Global optimization with polynomials and the problem of moments
Jean B Lasserre. 2001 · 2001
Earlier work this paper cites.
Sylvester–Habicht sequences and fast Cauchy index computation
Thomas Lickteig and Marie-Francoise Roy. 2001 · 2001
Earlier work this paper cites.
Accuracy and stability of numerical algorithms
Nicholas J Higham. 2002 · 2002
Cited alongside, same era.
Computing sum of squares decompositions with rational coefficients
Helfried Peyrl and Pablo A Parrilo. 2008 · 2008
Cited alongside, same era.
Efficient and accurate computation of upper bounds of approximation errors
Sylvain Chevillard, John Harrison, Mioara Joldeş, and Christoph Lauter. 2011 · 2011
Cited alongside, same era.
Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions. In Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation . 195–202
Feng Guo, Erich L Kaltofen, and Lihong Zhi. 2012 · 2012
Cited alongside, same era.
Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
Erich L Kaltofen, Bin Li, Zhengfeng Yang, and Lihong Zhi. 2012 · 2012
Cited alongside, same era.
JuMP: A modeling language for mathematical optimization
Iain Dunning, Joey Huchette, and Miles Lubin. 2017 · 2017
Later among the works it cites.
Bit complexity for multi-homogeneous polynomial system solving–Application to polynomial minimization
Mohab Safey El Din and Éric Schost. 2018 · 2018
Later among the works it cites.
Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials
Victor Magron, Mohab Safey El Din, and Markus Schweighofer. 2019a · 2019
Later among the works it cites.
A second order cone characterization for sums of nonnegative circuits. In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation . 450–457
Jie Wang and Victor Magron. 2020 · 2020
Later among the works it cites.
On moment approximation and the effective Putinar’s Positivstellensatz
Lorenzo Baldi and Bernard Mourrain. 2021 · 2021
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
General complex polynomial root solver and its further optimization for binary microlenses
Jan Skowron and Andrew Gould. 2012 · 2012
Cited alongside, same era.
Handbook of semidefinite programming: theory, algorithms, and applications . Vol. 27
Henry Wolkowicz, Romesh Saigal, and Lieven Vandenberghe. 2012 · 2012
Cited alongside, same era.
Solving secular and polynomial equations: A multiprecision algorithm
Dario A Bini and Leonardo Robol. 2014 · 2014
Cited alongside, same era.
From approximate factorization to root isolation with application to cylindrical algebraic decomposition
Kurt Mehlhorn, Michael Sagraloff, and Pengming Wang. 2015 · 2015
Cited alongside, same era.
Julia: A fresh approach to numerical computing
Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B Shah. 2017 · 2017
Cited alongside, same era.
Positive trigonometric polynomials and signal processing applications
Bogdan Dumitrescu. 2017 · 2017
Cited alongside, same era.
Calcul des indices des fonctions
Augustin-Louis Cauchy. 1832
Cited in the paper.
Msolve: A library for solving polynomial systems. In Proceedings of ISSAC . 51–58
Jérémy Berthomieu, Christian Eder, and Mohab Safey El Din. 2021 · 2021
Later among the works it cites.
The sum-of-squares hierarchy on the sphere and applications in quantum information theory
Kun Fang and Hamza Fawzi. 2021 · 2021
Later among the works it cites.
Univariate rational sums of squares
Teresa Krick, Bernard Mourrain, and Agnes Szanto. 2021 · 2021
Later among the works it cites.
Sum of squares decompositions of polynomials over their gradient ideals with rational coefficients
Victor Magron, Mohab Safey El Din, and Trung-Hieu Vu. 2021 · 2021
Later among the works it cites.
On exact Reznick, Hilbert-Artin and Putinar’s representations
Victor Magron and Mohab Safey El Din. 2021 · 2021
Later among the works it cites.
On the complexity of Putinar–Vasilescu’s Positivstellensatz
Ngoc Hoang Anh Mai and Victor Magron. 2022 · 2022
Closest in time.