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Precisely, given a target rank $r$, instead of optimizing on the manifold of rank $r$ matrices, we allow our interim estimated matrix to have a specific over-parametrized rank $2r$ structure. Our algorithm, denoted R2RILS for rank $2r$ iterative least squares, has low memory requirements, and at each iteration it solves a computationally cheap sparse least-squares problem. We motivate our algorithm by its theoretical analysis for the simplified case of a rank-1 matrix. Empirically, R2RILS is able to recover ill conditioned low rank matrices from very few observations -- near the information limit, and it is stable to additive noise.","url_abs":"https://arxiv.org/abs/2002.01849v1","url_pdf":"https://arxiv.org/pdf/2002.01849v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"rank-2r-iterative-least-squares-efficient","repo_url":"https://github.com/Jonathan-WIS/R2RILS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"rank-2r-iterative-least-squares-efficient","repo_url":"https://github.com/ckuemmerle/MatrixIRLS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"rank-2r-iterative-least-squares-efficient","repo_url":"https://github.com/pizilber/R2RILS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2002.01849","atlas_url":"https://app.syntology.ai/?focus=2002.01849","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.01849"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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