74 citations · 668 across the 48 of their papers we have counts for
7 papers · 1 filter
Semidefinite programming in matrix unknowns which are dimension free
J. William Helton, Igor Klep, Scott McCullough
One of the main applications of semidefinite programming lies in linear systems and control theory. Many problems in this subject, certainly the textbook classics, have matrices as…
A Non-commutative Real Nullstellensatz Corresponds to a Non-commutative Real Ideal; Algorithms
Jaka Cimpric, Bill Helton, Scott McCullough +1
This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commu…
A Semidefinite Approach for Truncated K-Moment Problems
J. William Helton, Jiawang Nie
A truncated moment sequence (tms) of degree d is a vector indexed by monomials whose degree is at most d. Let K be a semialgebraic set.The truncated K-moment problem (TKMP) is: whe…
The possible shapes of numerical ranges
J. William Helton, Ilya M. Spitkovsky
Which convex subsets of the complex plane are the numerical range W(A of some matrix A? This paper gives a precise characterization of these sets. In addition to this we show that…
The convex Positivstellensatz in a free algebra
J. William Helton, Igor Klep, Scott McCullough
Given a monic linear pencil L in g variables let D_L be its positivity domain, i.e., the set of all g-tuples X of symmetric matrices of all sizes making L(X) positive semidefinite.…
Noncommutative Plurisubharmonic Polynomials Part II: Local Assumptions
Jeremy M. Greene
We say that a symmetric noncommutative polynomial in the noncommutative free variables (x_1, x_2, ..., x_g) is noncommutative plurisubharmonic on a noncommutative open set if it ha…