20 citations · 31 across the 23 of their papers we have counts for
23 papers
Noncommutative Rational Sums of Squares in Free Algebras
Sizhuo Yan, Jianting Yang, Lihong Zhi
This paper introduces rational sums of squares for symmetric noncommutative polynomials in free algebras. Under the assumption that the polynomial admits a strictly positive scalar…
Two-step Newton's method for deflation-one singular zeros of analytic systems
Kisun Lee, Nan Li, Lihong Zhi
We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity.…
The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true
Hao Liang, Sizhuo Yan, Jianting Yang +1
Klep and Schweighofer asked whether the Nirgendsnegativsemide-finitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operat…
A Field-Theoretic View of Unlabeled Sensing
Hao Liang, Jingyu Lu, Manolis C. Tsakiris +1
Unlabeled sensing is the problem of solving a linear system of equations, where the right-hand-side vector is known only up to a permutation. In this work, we study fields of ratio…
Lower Bounds of Functions on Finite Abelian Groups
Jiangting Yang, Ke Ye, Lihong Zhi
The problem of computing the optimum of a function on a finite set is an important problem in mathematics and computer science. Many combinatorial problems such as MAX-SAT and MAXC…
A Characterization of Perfect Strategies for Mirror Games
Sizhuo Yan, Jianting Yang, Tianshi Yu +1
We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization o…