Using the QR Factorization to swiftly update least squares problems

Abstract: In this paper we study how to update the solution of the linear system Ax = b after the matrix A is changed by addition or deletion of rows or columns. Studying the QR Factorization of the system, more specifically, the factorization created by the Householder reflection algorithm, we find that we can split the algorithm in two parts. The result from the first part is trivial to update and is the only dependency for calculating the second part. We find that not only can this save a considerable amount of time when solving least squares problems but the algorithm is also very easy to implement.