Repeated QR Updating Algorithm for Solution of Equality Constrained Linear Least Squares Problems

Abstract

We consider a repeated QR updating algorithm for the solution of equality constrained linear least squares problems. The constrained problem is first converted into the linear least squares problem using weighted factor and then it is partitioned into a small well-manageable problem by removing a pair of blocks of rows and columns. We perform the QR factorization of the small subproblem and then it is updated by appending the removed data. The proposed strategy is effective for large scale dense problems and also particulary suitable for parallel implementation due to its partitioning by using the number of passes. Some numerical experiments are given to illustrate the accuracy of the proposed algorithm and the results are compared with the solution obtained through the nullspace method.