Is your numerical algorithm failing on rank-deficient problems? This paper addresses shortcomings in Algorithm 587, specifically within the WNNLS subroutine. The authors expose how these deficiencies can lead to errors, particularly when solving rank-deficient problems. The research offers five targeted improvements designed to enhance the algorithm's robustness and accuracy. The effectiveness of these changes is rigorously tested on four challenging rank-deficient test problems, showcasing their ability to mitigate the original issues. It's emphasized that, despite these improvements, WNNLS remains sensitive to poor problem scaling. This work provides essential insights for users of Algorithm 587, offering practical modifications to improve its reliability in specific scenarios. However, it warns about the possibility of bad scaling of the problem.
Appearing in ACM Transactions on Mathematical Software, this "Remark" directly addresses a pre-existing algorithm published in the journal. By identifying and correcting shortcomings in Algorithm 587, the paper contributes to the ongoing improvement and refinement of mathematical software. This focus aligns perfectly with the journal's goals.