 Regularized randomized iterative algorithms for factorized linear systemsKui Du Applied Mathematics and Computation, 2024, vol. 466, issue C Abstract: Randomized iterative algorithms for solving the factorized linear system, ABx=b with A∈Rm×ℓ, B∈Rℓ×n, and b∈Rm, have recently been proposed. They take advantage of the factorized form and avoid forming the matrix C=AB explicitly. However, they can only find the minimum norm (least squares) solution. In contrast, the regularized randomized Kaczmarz (RRK) algorithm can find solutions with certain structures from consistent linear systems. In this work, by combining the randomized Kaczmarz algorithm or the randomized Gauss–Seidel algorithm with the RRK algorithm, we propose two new regularized randomized iterative algorithms to find (least squares) solutions with certain structures of ABx=b. We prove linear convergence of the new algorithms. Computed examples are given to illustrate that the new algorithms can find sparse (least squares) solutions of ABx=b and can be better than the existing randomized iterative algorithms for the corresponding full linear system Cx=b with C=AB. Keywords: Factorized linear systems; Randomized Kaczmarz; Randomized Gauss–Seidel; Linear convergence; Sparse (least squares) solutions (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:466:y:2024:i:c:s0096300323006379 DOI: 10.1016/j.amc.2023.128468 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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