Positive Semi Definite

Positive semi-definite (PSD) matrices, characterized by having non-negative eigenvalues, are central to numerous scientific fields due to their representation of covariance structures and their role in various optimization problems. Current research focuses on efficient algorithms for handling large PSD matrices, including iterative solvers with warm starts for improved speed and novel clustering techniques that preserve crucial eigenstructural information. These advancements are impacting diverse applications, from machine learning (e.g., improving the efficiency of deep learning optimization and kernel methods) to statistical inference (e.g., enabling more robust probabilistic regression and entropy calculations). The development of computationally efficient methods for sampling and analyzing PSD matrices is a key theme driving progress in this area.