{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/accurate-eigenvalue-decomposition-of","title":"Accurate eigenvalue decomposition of arrowhead matrices and applications","arxiv_id":"1302.7203","date":"2013-02-28","proceeding":null,"authors":["Nevena Jakovcevic Stor","Ivan Slapnicar","Jesse L. Barlow"],"abstract":"We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$ operations. The algorithm is based on a shift-and-invert approach. Double precision is eventually needed to compute only one element of the inverse of the shifted matrix. Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing. Our results extend to Hermitian arrowhead matrices, real symmetric diagonal-plus-rank-one matrices and singular value decomposition of real triangular arrowhead matrices.","url_abs":"http://arxiv.org/abs/1302.7203v3","url_pdf":"http://arxiv.org/pdf/1302.7203v3.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":"accurate-eigenvalue-decomposition-of","repo_url":"https://github.com/UnofficialJuliaMirror/Arrowhead.jl-1a029416-38b0-5245-b7ed-67249edcb994","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"accurate-eigenvalue-decomposition-of","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/Arrowhead.jl-1a029416-38b0-5245-b7ed-67249edcb994","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"accurate-eigenvalue-decomposition-of","repo_url":"https://github.com/ivanslapnicar/Arrowhead.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}