Hoon Hong

collaborators

4 papers

math.RA2026

Certificate for Orthogonal Equivalence of Real Polynomials by Polynomial-Weighted Principal Component Analysis

Martin Helmer, David Hong, Hoon Hong

Suppose that $f (x) \in R [x_{1}, \dots, x_{n}]$ and $g (x) \in R [x_{1}, \dots, x_{n}]$ are two real polynomials of degree $d$ in $n$ variables. If the polynomials $f$ and $g$ …

math.AG2024

Equi-affine minimal-degree moving frames for polynomial curves

Hoon Hong, Irina A. Kogan

We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-pr…

math.OC2024

Almost Bijective Parametrization of Copositive Univariate Polynomials

Hoon Hong, Ezra Nance

In this work we develop a novel recursive method for parametrizing the cone of copositive univariate polynomials of any arbitrary degree $d$ . This parametrization is surjective, al…

math.OC2024

Almost Bijective Parametrization of $3 \times 3$ Copositive Matrices

Hoon Hong, Ezra Nance

In this work we take a deep dive into the cone of copositive $3 \times 3$ matrices. In doing so we visualize the cone, make geometric observations about it, and prove them. We then…

Certificate for Orthogonal Equivalence of Real Polynomials by Polynomial-Weighted Principal Component Analysis

Equi-affine minimal-degree moving frames for polynomial curves

Almost Bijective Parametrization of Copositive Univariate Polynomials

Almost Bijective Parametrization of 3×3 Copositive Matrices

Almost Bijective Parametrization of $3 \times 3$ Copositive Matrices