Markus Schweighofer

1.0k total citations
22 papers, 477 citations indexed

About

Markus Schweighofer is a scholar working on Computational Theory and Mathematics, Numerical Analysis and Algebra and Number Theory. According to data from OpenAlex, Markus Schweighofer has authored 22 papers receiving a total of 477 indexed citations (citations by other indexed papers that have themselves been cited), including 17 papers in Computational Theory and Mathematics, 12 papers in Numerical Analysis and 7 papers in Algebra and Number Theory. Recurrent topics in Markus Schweighofer's work include Advanced Optimization Algorithms Research (12 papers), Polynomial and algebraic computation (11 papers) and Advanced Topics in Algebra (6 papers). Markus Schweighofer is often cited by papers focused on Advanced Optimization Algorithms Research (12 papers), Polynomial and algebraic computation (11 papers) and Advanced Topics in Algebra (6 papers). Markus Schweighofer collaborates with scholars based in Germany, France and Slovenia. Markus Schweighofer's co-authors include Jiawang Nie, Igor Klep, Tim Netzer, Victor Magron, Mohab Safey El Din, Claus Scheiderer, Ken Dykema, Hans‐Jürgen Bandelt, Thomas Sonar and Sebastian Walcher and has published in prestigious journals such as Journal of Statistical Physics, Advances in Mathematics and SIAM Journal on Optimization.

In The Last Decade

Markus Schweighofer

20 papers receiving 413 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Markus Schweighofer Germany 11 378 316 72 69 54 22 477
Jiyuan Tao United States 11 425 1.1× 331 1.0× 160 2.2× 63 0.9× 27 0.5× 41 487
Roman Sznajder United States 10 544 1.4× 440 1.4× 134 1.9× 43 0.6× 48 0.9× 27 611
Zhonggang Zeng United States 11 383 1.0× 156 0.5× 69 1.0× 48 0.7× 156 2.9× 29 477
Panayiotis Psarrakos Greece 12 379 1.0× 181 0.6× 70 1.0× 50 0.7× 25 0.5× 60 454
Xingping Sheng China 12 306 0.8× 206 0.7× 20 0.3× 21 0.3× 25 0.5× 27 351
Yifen Ke China 10 340 0.9× 262 0.8× 20 0.3× 26 0.4× 61 1.1× 52 396
K. C. ‎Sivakumar India 8 220 0.6× 95 0.3× 48 0.7× 41 0.6× 23 0.4× 78 270
King-wah Eric Chu United Kingdom 10 328 0.9× 203 0.6× 25 0.3× 35 0.5× 17 0.3× 15 419
Hristo S. Sendov Canada 9 198 0.5× 142 0.4× 19 0.3× 63 0.9× 118 2.2× 34 375
Hermann Schichl Austria 10 140 0.4× 96 0.3× 78 1.1× 131 1.9× 19 0.4× 36 375

Countries citing papers authored by Markus Schweighofer

Since Specialization
Citations

This map shows the geographic impact of Markus Schweighofer's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Markus Schweighofer with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Markus Schweighofer more than expected).

Fields of papers citing papers by Markus Schweighofer

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Markus Schweighofer. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Markus Schweighofer. The network helps show where Markus Schweighofer may publish in the future.

Co-authorship network of co-authors of Markus Schweighofer

This figure shows the co-authorship network connecting the top 25 collaborators of Markus Schweighofer. A scholar is included among the top collaborators of Markus Schweighofer based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Markus Schweighofer. Markus Schweighofer is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Schweighofer, Markus, et al.. (2024). Sum-of-Squares Certificates for Copositivity via Test States. SPIRE - Sciences Po Institutional REpository. 8(4). 797–820.
2.
Schweighofer, Markus, et al.. (2023). Amalgamation of real zero polynomials. Indagationes Mathematicae. 35(1). 37–59.
3.
Magron, Victor, Mohab Safey El Din, & Markus Schweighofer. (2018). Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials. Journal of Symbolic Computation. 93. 200–220. 10 indexed citations
4.
Schweighofer, Markus, et al.. (2018). On the Exactness of Lasserre Relaxations for Compact Convex Basic Closed Semialgebraic Sets. SIAM Journal on Optimization. 28(2). 1796–1816. 4 indexed citations
5.
Kühnel, Wolfgang, et al.. (2015). Zur neuen Schulmathematik im Abitur – Die Bildungsstandards der KMK von 2012. Mitteilungen der Deutschen Mathematiker-Vereinigung. 23(2). 2 indexed citations
6.
Dykema, Ken, et al.. (2013). Addendum to “Connesʼ embedding conjecture and sums of hermitian squares” [Adv. Math. 217 (4) (2008) 1816–1837]. Advances in Mathematics. 252. 805–811. 3 indexed citations
7.
Scheiderer, Claus, et al.. (2012). Pure states, nonnegative polynomials and sums of squares. Commentarii Mathematici Helvetici. 87(1). 113–140. 5 indexed citations
8.
Netzer, Tim, et al.. (2010). Exposed Faces of Semidefinitely Representable Sets. SIAM Journal on Optimization. 20(4). 1944–1955. 12 indexed citations
9.
Klep, Igor & Markus Schweighofer. (2010). Pure states, positive matrix polynomials and sums of hermitian squares. Indiana University Mathematics Journal. 59(3). 857–874. 15 indexed citations
10.
Schweighofer, Markus. (2009). Describing convex semialgebraic sets by linear matrix inequalities. 385–386. 1 indexed citations
11.
Klep, Igor & Markus Schweighofer. (2008). Sums of Hermitian Squares and the BMV Conjecture. Journal of Statistical Physics. 133(4). 739–760. 22 indexed citations
12.
Klep, Igor & Markus Schweighofer. (2007). Connes' embedding conjecture and sums of hermitian squares. Advances in Mathematics. 217(4). 1816–1837. 47 indexed citations
13.
Netzer, Tim, et al.. (2007). A note on the representation of positive polynomials with structured sparsity. Archiv der Mathematik. 89(5). 399–403. 19 indexed citations
14.
Nie, Jiawang & Markus Schweighofer. (2006). On the complexity of Putinar's Positivstellensatz. Journal of Complexity. 23(1). 135–150. 93 indexed citations
15.
Schweighofer, Markus. (2006). Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares. SIAM Journal on Optimization. 17(3). 920–942. 45 indexed citations
16.
Schweighofer, Markus. (2005). Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets. manuscripta mathematica. 117(4). 407–428. 9 indexed citations
17.
Schweighofer, Markus. (2005). Optimization of Polynomials on Compact Semialgebraic Sets. SIAM Journal on Optimization. 15(3). 805–825. 92 indexed citations
18.
Schweighofer, Markus. (2004). On the complexity of Schmüdgen's Positivstellensatz. Journal of Complexity. 20(4). 529–543. 46 indexed citations
19.
Schweighofer, Markus. (2003). Iterated rings of bounded elements and generalizations of Schmüdgens Positivstellensatz. Journal für die reine und angewandte Mathematik (Crelles Journal). 2003(554). 17 indexed citations
20.
Schweighofer, Markus. (2002). An algorithmic approach to Schmüdgen's Positivstellensatz. Journal of Pure and Applied Algebra. 166(3). 307–319. 24 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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