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Eric Evert

Department of Mathematics

Publications and Preprints

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

Publications

  1. On best low rank approximation of positive definite tensors (with L. De Lathauwer) SIAM J. Matrix Anal. Appl.
  2. Convexity of a certain operator trace functional (with S. McCullough, T. Štrekelj, and A. Vershynina) Linear Algebra Appl.
  3. Canonical Polyadic Decomposition via the generalized Schur decomposition (with M. Vandecappelle and L. De Lathauwer) IEEE J. Signal Process. Lett.
  4. Guarantees for the existence of best low rank tensor approximations (with L. De Lathauwer) SIAM J. Matrix Anal. Appl.
  5. A recursive eigenspace computation for the canonical polyadic decomposition (with M. Vandecappelle and L. De Lathauwer) SIAM J. Matrix Anal. Appl.
  6. The Arveson boundary of a free quadrilateral is given by a noncommutative variety Operators and Matrices.
  7. Empirical properties of optima in free semidefinite programs (with Y. Fu, J.W. Helton, and J. Yin) Experimental Mathematics.
  8. Efficient evaluation of noncommutative polynomials using tensor and noncommutative Waring decompositions (with J.W. Helton, S. Huang, and J. Nie) Numer. Funct. Anal. Optim.
  9. Arveson extreme points span free spectrahedra (with J.W. Helton) Math. Ann.
  10. Matrix convex sets without absolute extreme points Linear Algebra Appl.
  11. Extreme points of matrix convex sets, free spectrahedra and dilation theory (with J.W. Helton, I. Klep, and S. McCullough.) J. of Geom. Anal.
  12. Circular free spectrahedra (with J.W. Helton, I. Klep, and S. McCullough) J. Math. Anal. Appl.
  13. 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

Preprints

  1. Matrix extreme points and free extreme points of free spectrahedra (with A. Epperly, J.W. Helton, and I. Klep)
  2. Decomposition of a tensor into multilinear rank-$(M_r,N_r,\cdot)$ terms (with I. Domanov, N. Vervliet, and L. De Lathauwer)

Conference Papers

  1. CPD computation via recursive eigenspace decompositions (with M. Vandecappelle and L. De Lathauwer) Presented at IEEE International Conference on Acoustics, Speech, and Signal Processing, May 2022.
  2. 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) Accepted to IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, December 2023.

Submitted Conference Papers

  1. New Tools for Smoothed Analysis: Least Singular Value Bounds for Random Matrices with Dependent Entries (with A. Bhaskara, V. Srinivas, A. Vijayaraghavan) Submitted to Annual ACM Symposium on Theory of Computing 2024

Programming

  1. NCSE 2.3: An NCAlgebra package for optimization over free spectrahedra (with M. de Oliveria, J. Yin, and J.W. Helton)

Science Communication

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