10 citations · 14 across the 5 of their papers we have counts for
8 papers
Pure states, nonnegative polynomials and sums of squares
Sabine Burgdorf, Claus Scheiderer, Markus Schweighofer
In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial on a basic closed semialgebrai…
On the complexity of Putinar's Positivstellensatz
Jiawang Nie, Markus Schweighofer
We prove an upper bound on the degree complexity of Putinar's Positivstellensatz. This bound is much worse than the one obtained previously for Schmüdgen's Positivstellensatz but i…
A Gröbner basis proof of the flat extension theorem for moment matrices
Markus Schweighofer
This paper has been withdrawn by the author since in Lemma 2 is in general not a subspace.
A note on the representation of positive polynomials with structured sparsity
David Grimm, Tim Netzer, Markus Schweighofer
We consider real polynomials in finitely many variables. Let the variables consist of finitely many blocks that are allowed to overlap in a certain way. Let the solution set of a f…
Global optimization of polynomials using gradient tentacles and sums of squares
Markus Schweighofer
In this work, the combine the theory of generalized critical values with the theory of iterated rings of bounded elements (real holomorphy rings). We consider the problem of comput…
Iterated rings of bounded elements: Erratum
Markus Schweighofer
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schmüdgen's theorem" [1] and in the author's article "It…