116 citations · 258 across the 22 of their papers we have counts for
24 papers
Amalgamation of real zero polynomials
David Sawall, Markus Schweighofer
With this article, we hope to launch the investigation of what we call the real zero amalgamation problem. Whenever a polynomial arises from another polynomial by substituting zero…
Real Algebraic Geometry, Positivity and Convexity
Markus Schweighofer
Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algeb…
Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients
Victor Magron, Mohab Safey El Din, Markus Schweighofer +1
Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing. It is well known from the Riesz-Fejéz spectral…
Spectrahedral relaxations of hyperbolicity cones
Markus Schweighofer
Let be a real zero polynomial in variables. Then defines a rigidly convex set . We construct a linear matrix inequality of size in the same variables th…
Generalized eigenvalue methods for Gaussian quadrature rules
Grigoriy Blekherman, Mario Kummer, Cordian Riener +2
A quadrature rule of a measure on the real line represents a convex combination of finitely many evaluations at points, called nodes, that agrees with integration against f…
On the exactness of Lasserre relaxations and pure states over real closed fields
Tom-Lukas Kriel, Markus Schweighofer
Consider a finite system of non-strict polynomial inequalities with solution set . Its Lasserre relaxation of degree is a certain natural linear matrix i…