J. William Helton

Mathematical Physics · 2003–2014

A researcher in the Science corpus: 12 papers; trusts 17 researchers and is trusted by 23 researchers here, as inferred from the citation graph.

Subfields

• Mathematical Physics — 39 citations into it; #2,908 of 8,562 by trust here, #2,682 by citations
• Computational Theory and Mathematics — 35 citations into it; #1,231 of 12,182 by trust here, #2,015 by citations
• Applied Mathematics — 33 citations into it; #829 of 7,620 by trust here, #1,096 by citations
• Algebra and Number Theory — 31 citations into it; #2,156 of 2,864 by trust here, #1,608 by citations
• Numerical Analysis — 26 citations into it; #438 of 3,586 by trust here, #561 by citations
• Geometry and Topology — 21 citations into it; #4,311 of 7,422 by trust here, #5,008 by citations
• Control and Systems Engineering — 15 citations into it
• Statistics and Probability — 15 citations into it

Whom J. William Helton trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Pablo A. Parrilo
2. D. Voiculescu
3. Juan F. Camino
4. Gelu Popescu
5. Vern I. Paulsen
6. Stephen Prajna
7. Scott McCullough
8. Jean B. Lasserre
9. Yurii E. Nesterov
10. K. Schmuedgen

Who trusts J. William Helton overall

1. Victor Vinnikov
2. Petter Brand'en
3. Adam W. Marcus
4. Dmitry S. Kaliuzhnyi-Verbovetskyi
5. Julius Borcea
6. Joseph A. Ball
7. Jim Agler
8. Gelu Popescu
9. Greg W. Anderson
10. Tim Netzer

Papers from J. William Helton's perspective

Ordered by how strongly the researchers J. William Helton trusts endorse each paper. Same corpus, a different order for every researcher.

1. A unified algebraic approach to linear control design: Robert E. Skelton, Tetsuya Iwasaki and Karolos M. Grigoriadis; Copyright Taylor & Francis, 1998, ISBN: 0-7484-0592-5 (at - Automatisierungstechnik)
2. GloptiPoly: global optimization over polynomials with Matlab and SeDuMi (Proceedings of the 41st IEEE Conference on Decision and Control, 2002.)
3. Free analysis questions I: duality transform for the coalgebra of ∂X:B
4. Spherical contractions and interpolation problems on the unit ball
5. Pick Interpolation and Hilbert Function Spaces
6. Minimizing Polynomial Functions (Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science)
7. Matrix Inequalities: A Symbolic Procedure to Determine Convexity Automatically (Integral equations and operator theory)
8. Semidefinite Optimization and Convex Algebraic Geometry
9. Basic Algebraic Geometry
10. The convex Positivstellensatz in a free algebra

Their papers

• Linear matrix inequality representation of sets (2003) — 415 citations
• Matrix Inequalities: A Symbolic Procedure to Determine Convexity Automatically (2003) — 60 citations
• Every convex free basic semi-algebraic set has an LMI representation (2012) — 105 citations
• NONCOMMUTATIVE CONVEXITY ARISES FROM LINEAR MATRIX INEQUALITIES. (2006) — 136 citations
• Operator-valued Semicircular Elements: Solving A Quadratic Matrix Equation with Positivity Constraints (2007) — 120 citations
• POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION (2006) — 59 citations
• The Tracial Hahn-Banach Theorem, Polar Duals, Matrix Convex Sets, and Projections of Free Spectrahedra (2014) — 48 citations
• Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions (2014) — 63 citations
• A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: Algorithms (2011) — 49 citations
• Proper analytic free maps (2010) — 79 citations
• Engineering Systems and Free Semi-Algebraic Geometry (2009) — 64 citations
• Analytic mappings between noncommutative pencil balls (2009) — 62 citations