Publications and preprints

Click here for a list of publications of available on ArXiv.

Publications

• Extreme points of matrix convex sets and their spanning properties (with B. Passer and T. Štrekelj) Operator Theory, Springer
• Free extreme points span generalized free spectrahedra given by compact coefficients J. Math. Anal. Appl.
• Decomposition of a tensor into multilinear rank-$(M_r,N_r,\cdot)$ terms (with I. Domanov, N. Vervliet, and L. De Lathauwer) SIAM J. Matrix Anal. Appl.
• Matrix extreme points and free extreme points of free spectrahedra (with A. Epperly, J.W. Helton, and I. Klep) Optim. Method. Softw.
• On best low rank approximation of positive definite tensors (with L. De Lathauwer) SIAM J. Matrix Anal. Appl.
• Convexity of a certain operator trace functional (with S. McCullough, T. Štrekelj, and A. Vershynina) Linear Algebra Appl.
• Canonical Polyadic Decomposition via the generalized Schur decomposition (with M. Vandecappelle and L. De Lathauwer) IEEE J. Signal Process. Lett.
• Guarantees for the existence of best low rank tensor approximations (with L. De Lathauwer) SIAM J. Matrix Anal. Appl.
• A recursive eigenspace computation for the canonical polyadic decomposition (with M. Vandecappelle and L. De Lathauwer) SIAM J. Matrix Anal. Appl.
• The Arveson boundary of a free quadrilateral is given by a noncommutative variety Operators and Matrices.
• Empirical properties of optima in free semidefinite programs (with Y. Fu, J.W. Helton, and J. Yin) Experimental Mathematics.
• Efficient evaluation of noncommutative polynomials using tensor and noncommutative Waring decompositions (with J.W. Helton, S. Huang, and J. Nie) Numer. Funct. Anal. Optim.
• Arveson extreme points span free spectrahedra (with J.W. Helton) Math. Ann.
• Matrix convex sets without absolute extreme points Linear Algebra Appl.
• Extreme points of matrix convex sets, free spectrahedra and dilation theory (with J.W. Helton, I. Klep, and S. McCullough.) J. of Geom. Anal.
• Circular free spectrahedra (with J.W. Helton, I. Klep, and S. McCullough) J. Math. Anal. Appl.
• Factor postes of frames and duals in finite dimensions (with M.S. Copenhaver, Y.H Kim, T. Klingler, S.K. Narayan, and S.T. Nghiem) Involve

Conference Papers

• New Tools for Smoothed Analysis: Least Singular Value Bounds for Random Matrices with Dependent Entries (with A. Bhaskara, V. Srinivas, A. Vijayaraghavan) STOC 2024
• CPD computation via recursive eigenspace decompositions (with M. Vandecappelle and L. De Lathauwer) IEEE International Conference on Acoustics, Speech, and Signal Processing, May 2022.
• Uniqueness result and algebraic algorithm for decomposition into multilinear rank-$(M_r,N_r,\cdot)$ terms and joint block diagonalization (with I. Domanov, N. Vervliet, and L. De Lathauwer) IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, December 2023.

Preprints

• Matrix convex sets over the Euclidean ball and polar duals of real free spectrahedra (with B. Passer)

Programming

• NCSE 3.1.2: An NCAlgebra package for optimization over free spectrahedra (with A. Epperly, M. de Oliveria, J. Yin, and J.W. Helton)

Science Communication

• Tensors and multilinear algebra: what and why (with L. De Lauthawer) Leuven.AI Stories