Block Updating/Downdating Algorithms for Regularised Least Squares Problems and Applications to Linear Discriminant Analysis

Abstract

Block updating and downdating algorithms for regularised least squares problems with multiple right-hand sides based on the economical $QR$ decomposition are proposed. They exploit the initial coefficient matrix structure and use existing solution to establish a solution of the amended problem. Such an approach demonstrates its efficiency in terms of the memory required and the computational cost. Applications to linear discriminant analysis are considered and numerical experiments involving real-world databases show the efficiency of the methods.