Cholesky Factorization

Cholesky factorization, the decomposition of a positive definite matrix into a lower triangular matrix and its transpose, is a fundamental linear algebra technique with applications across diverse scientific fields. Current research focuses on improving its numerical stability and efficiency, particularly in high-dimensional settings and for specific applications like vision-aided inertial navigation and Gaussian process inference, often employing preconditioning techniques or novel metrics on Cholesky manifolds to achieve this. These advancements lead to faster and more robust algorithms for solving linear systems, recovering causal models, and optimizing machine learning models, impacting fields ranging from robotics to statistical inference.