{"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/computing-truncated-joint-approximate","title":"Computing Truncated Joint Approximate Eigenbases for Model Order Reduction","arxiv_id":"2201.05928","date":"2022-01-15","proceeding":null,"authors":["Terry A. Loring","Fredy Vides"],"abstract":"In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented. More specifically, given a finite collection $X_1,\\ldots,X_d$ of Hermitian matrices in $\\mathbb{C}^{n\\times n}$, a positive integer $r\\ll n$, and a collection of complex numbers $\\hat{x}_{j,k}\\in \\mathbb{C}$ for $1\\leq j\\leq d$, $1\\leq k\\leq r$. First, we study the computability of a set of $r$ vectors $w_1,\\ldots,w_r\\in \\mathbb{C}^{n}$, such that $w_k=\\arg\\min_{w\\in \\mathbb{C}^n}\\sum_{j=1}^d\\|X_jw-\\hat{x}_{j,k} w\\|^2$ for each $1\\leq k \\leq r$, then we present a model order reduction procedure based on the truncated joint approximate eigenbases computed with the aforementioned techniques. Some prototypical algorithms together with some numerical examples are presented as well.","url_abs":"https://arxiv.org/abs/2201.05928v2","url_pdf":"https://arxiv.org/pdf/2201.05928v2.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":"computing-truncated-joint-approximate","repo_url":"https://github.com/fredyvides/pytjae","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"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}