Strengths and limitations of stretching for least-squares problems with some dense rows

Scott, J. ORCID: https://orcid.org/0000-0003-2130-1091 and Tuma, M. (2020) Strengths and limitations of stretching for least-squares problems with some dense rows. ACM Transactions on Mathematical Software (TOMS), 47 (1). pp. 1-25. ISSN 0098-3500 doi: 10.1145/3412559

Abstract/Summary

We recently introduced a sparse stretching strategy for handling dense rows that can arise in large-scale linear least-squares problems and make such problems challenging to solve. Sparse stretching is designed to limit the amount of fill within the stretched normal matrix and hence within the subsequent Cholesky factorization. While preliminary results demonstrated that sparse stretching performs significantly better than standard stretching, it has a number of limitations. In this paper, we discuss and illustrate these limitations and propose new strategies that are designed to overcome them. Numerical experiments on problems arising from practical applications are used to demonstrate the effectiveness of these new ideas. We consider both direct and preconditioned iterative solvers.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/91971
Identification Number/DOI	10.1145/3412559
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	ACM
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