 Splitting-based randomized iterative methods for solving indefinite least squares problemYanjun Zhang and Hanyu Li Applied Mathematics and Computation, 2023, vol. 446, issue C Abstract: The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose a simple and effective splitting (SP) method according to its own structure, and prove that it converges for any initial value. Further, to avoid implementing some matrix multiplications and calculating the inverse of large matrix, and considering the acceleration and efficiency of the randomized strategy, we develop two randomized iterative methods on the basis of the SP method as well as the randomized Kaczmarz, Gauss-Seidel and coordinate descent methods, and describe their convergence properties. Numerical results show that our three methods all have quite decent performance in both computing time and iteration numbers compared with the latest iterative method of the ILS problem, and also demonstrate that the two randomized methods indeed yield significant acceleration in terms of computing time. Keywords: Indefinite least squares problem; Splitting method; Randomized method; Kaczmarz; Gauss-Seidel; Coordinate descent (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000619 DOI: 10.1016/j.amc.2023.127892 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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