QR Decomposition

QR decomposition is a matrix factorization technique that decomposes a matrix into an orthogonal matrix and an upper triangular matrix, primarily used to solve linear least squares problems and improve numerical stability in computations. Current research focuses on enhancing QR decomposition's efficiency and robustness in various applications, including Kalman filtering, vision-aided inertial navigation, and machine learning tasks like learned index structures and feature selection, often incorporating preconditioning or iterative refinement strategies. These advancements are impacting diverse fields, from improving the speed and accuracy of computer vision algorithms to enabling more efficient and privacy-preserving federated learning approaches.