2 papers
math.SP2026
Banded Hermitian Matrices, Matrix Orthogonal Polynomials, and the Toda Lattice
Charbel Abi Younes, Thomas Trogdon
We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure…
math.ST2025
A Lanczos-Based Algorithmic Approach for Spike Detection in Large Sample Covariance Matrices
Charbel Abi Younes, Xiucai Ding, Thomas Trogdon
We introduce a new approach for estimating the number of spikes in a general class of spiked covariance models without directly computing the eigenvalues of the sample covariance m…