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Persistent URL http://purl.org/net/epubs/work/47616406
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Record Id 47616406
Title A computational study of using black-box QR solvers for large-scale sparse-dense linear least squares problems
Abstract Large-scale overdetermined linear least squares problems arise in many practical applications, both as subproblems of nonlinear least squares problems and in their own right. One popular solution method is based on the backward stable QR factorization of the system matrix A. This paper focuses on sparse-dense linear least squares problems, that is, problems where A is sparse except from a small number of rows that are considered to be dense. For large-scale problems, the direct application of a QR solver will fail because of a lack of memory or will be unacceptably slow. We study a number of approaches for solving such problems using a sparse QR solver without modication. We consider the case where the sparse part of A is rank-decient and show that either preprocessing A using partial matrix stretching or using regularization and employing a direct-iterative approach can be seamlessly combined with a black-box QR solver. Furthermore, we propose extending the augmented system formulation with iterative renement for sparse problems to sparse-dense problems and demonstrate experimentally that multi-precision variants can be successfully used.
Organisation STFC , SCI-COMP
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Language English (EN)
Type Details URI(s) Local file(s) Year
Preprint RAL Preprints RAL-P-2020-004, ACM Trans Math Software STFC, 2020. RAL-P-2020-004.pdf 2020