Computational Experiments with Abs Algorithms for Overdetermined Linear Systems

TL;DR

This paper evaluates ABS algorithms for computing least-squares solutions to overdetermined linear systems by comparing Huang (and modified Huang) against the implicit QR variant, alongside LAPACK QR/SVD baselines, on a suite of ill-conditioned synthetic matrices. The study demonstrates that explicit QR methods are typically faster for well-conditioned problems, while the modified Huang and implicit QR variants excel on highly ill-conditioned matrices (notably IDF3), achieving rapid solutions and correct rank detection in many cases. The results provide practical guidance on when ABS methods offer advantages and document performance across 21 test problems, including breakdown occurrences for certain IDF2 instances and slowdowns for SVD-based routines. The Appendix provides granular per-problem data to support these conclusions.

Abstract

The results of computational experiments with ABS algorithms for overdetermined linear systems are reported.