{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T08:50:08Z","timestamp":1773219008121,"version":"3.50.1"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cam.2026.117543","type":"journal-article","created":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T07:59:34Z","timestamp":1772524774000},"page":"117543","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Nested quaternion matrix and recursive approach to its singular value decomposition"],"prefix":"10.1016","volume":"485","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1598-2223","authenticated-orcid":false,"given":"Qile","family":"Zhu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6383-7663","authenticated-orcid":false,"given":"Shiqian","family":"Wu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5718-7916","authenticated-orcid":false,"given":"Shoulie","family":"Xie","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3206-6384","authenticated-orcid":false,"given":"Zihang","family":"Yin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4601-4507","authenticated-orcid":false,"given":"Sos","family":"Agaian","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117543_bib0001","series-title":"Quaternion and Octonion Color Image Processing with MATLAB","author":"Grigoryan","year":"2018"},{"issue":"9","key":"10.1016\/j.cam.2026.117543_bib0002","doi-asserted-by":"crossref","first-page":"2056","DOI":"10.3390\/math11092056","article-title":"Review of quaternion-based color image processing methods","volume":"11","author":"Huang","year":"2023","journal-title":"Math"},{"issue":"6","key":"10.1016\/j.cam.2026.117543_bib0003","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MSP.2023.3278071","article-title":"Quaternions in signal and image processing: a comprehensive and objective overview","volume":"40","author":"Miron","year":"2023","journal-title":"IEEE Signal Process. Mag."},{"key":"10.1016\/j.cam.2026.117543_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2021.113494","article-title":"The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations","volume":"393","author":"Yu","year":"2021","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117543_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2022.114664","article-title":"The implicitly restarted multi-symplectic block-Lanczos method for large-scale hermitian quaternion matrix eigenvalue problem and applications","volume":"419","author":"Jia","year":"2023","journal-title":"J. Comput. Appl. Math."},{"issue":"108533","key":"10.1016\/j.cam.2026.117543_bib0006","first-page":"269","article-title":"Commutative quaternion algebra and DSP fundamental properties: quaternion convolution and Fourier transform","volume":"196","author":"Grigoryan","year":"2022","journal-title":"Signal Process."},{"key":"10.1016\/j.cam.2026.117543_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2014.11.019","article-title":"Quaternion Fourier transform based alpha-rooting method for color image measurement and enhancement","volume":"109","author":"Grigoryan","year":"2015","journal-title":"Signal Process."},{"issue":"4","key":"10.1016\/j.cam.2026.117543_bib0008","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/TIP.2015.2397314","article-title":"Vector sparse representation of color image using quaternion matrix analysis","volume":"24","author":"Xu","year":"2015","journal-title":"IEEE Trans. Image Process."},{"issue":"7","key":"10.1016\/j.cam.2026.117543_bib0009","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1016\/j.sigpro.2004.04.001","article-title":"Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing","volume":"84","author":"Bihan","year":"2004","journal-title":"Signal Process."},{"key":"10.1016\/j.cam.2026.117543_bib0010","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1109\/TIP.2019.2941319","article-title":"Low-rank quaternion approximation for color image processing","volume":"29","author":"Chen","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.cam.2026.117543_bib0011","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.neucom.2018.12.034","article-title":"Quaternion-based weighted nuclear norm minimization for color image denoising","volume":"332","author":"Yu","year":"2019","journal-title":"Neurocomputing"},{"issue":"8","key":"10.1016\/j.cam.2026.117543_bib0012","doi-asserted-by":"crossref","first-page":"3808","DOI":"10.1016\/j.jfranklin.2022.03.036","article-title":"Two dimensional quaternion valued singular spectrum analysis with application to image denoising","volume":"359","author":"Lin","year":"2022","journal-title":"J. Frankl. Inst."},{"key":"10.1016\/j.cam.2026.117543_bib0013","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TIP.2021.3128321","article-title":"Color image recovery using low-rank quaternion matrix completion algorithm","volume":"31","author":"Miao","year":"2021","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.cam.2026.117543_bib0014","doi-asserted-by":"crossref","first-page":"3868","DOI":"10.1109\/TIP.2022.3176133","article-title":"Non-local robust quaternion matrix completion for large-scale color image and video inpainting","volume":"31","author":"Jia","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.cam.2026.117543_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2023.108971","article-title":"Color image watermarking based on a fast structure-preserving algorithm of quaternion singular value decomposition","volume":"208","author":"Zhang","year":"2023","journal-title":"Signal Process."},{"key":"10.1016\/j.cam.2026.117543_bib0016","doi-asserted-by":"crossref","first-page":"3964","DOI":"10.1109\/TIP.2023.3293773","article-title":"Efficient robust watermarking based on structure-preserving quaternion singular value decomposition","volume":"32","author":"Chen","year":"2023","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.cam.2026.117543_bib0017","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.cam.2016.03.031","article-title":"Real structure-preserving algorithms of householder based transformations for quaternion matrices","volume":"305","author":"Li","year":"2016","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117543_bib0018","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1137\/21M1418319","article-title":"Randomized quaternion singular value decomposition for low-rank matrix approximation","volume":"44","author":"Liu","year":"2022","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2026.117543_bib0019","article-title":"Randomized low rank approximation for nonnegative pure quaternion matrices","volume":"150","author":"Lyu","year":"2024","journal-title":"Appl. Mathe. Lett."},{"key":"10.1016\/j.cam.2026.117543_bib0020","article-title":"A two-sided randomized algorithm for low-rank quaternion matrix approximation","volume":"171","author":"Ding","year":"2025","journal-title":"Appl. Mathe. Lett."},{"issue":"10","key":"10.1016\/j.cam.2026.117543_bib0021","doi-asserted-by":"crossref","first-page":"4246","DOI":"10.1109\/TAC.2020.3007332","article-title":"Quaternion-valued distributed filtering and control","volume":"65","author":"Talebi","year":"2020","journal-title":"IEEE Trans. Autom. Contr."},{"issue":"1","key":"10.1016\/j.cam.2026.117543_bib0022","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1109\/TAES.2024.3447631","article-title":"Adaptive quaternion state estimation for 3-D and 4-D signals with weighted maximum correntropy: a widely linear approach","volume":"61","author":"Lin","year":"2024","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"10.1016\/j.cam.2026.117543_bib0023","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2021.104450","article-title":"Octonion continuous orthogonal moments and their applications in color stereoscopic image reconstruction and zero-watermarking","volume":"106","author":"Wang","year":"2021","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.cam.2026.117543_bib0024","article-title":"Dual quaternion singular value decomposition based on bidiagonalization to a dual number matrix using dual quaternion householder transformations","volume":"152","author":"Ding","year":"2024","journal-title":"Appl. Mathe. Lett."},{"key":"10.1016\/j.cam.2026.117543_bib0025","article-title":"An unstructured algorithm for the singular value decomposition of biquaternion matrices","volume":"163","author":"Wang","year":"2025","journal-title":"Appl. Mathe. Lett."},{"issue":"2","key":"10.1016\/j.cam.2026.117543_bib0026","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s13366-012-0113-7","article-title":"Biquaternions and their complex matrix representations","volume":"54","author":"Tian","year":"2013","journal-title":"Beitr. Algebra Geom."},{"key":"10.1016\/j.cam.2026.117543_bib0027","series-title":"Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics","volume":"5","author":"Hestenes","year":"2012"},{"key":"10.1016\/j.cam.2026.117543_bib0028","series-title":"Quaternion Fourier Transforms for Signal and Image Processing","author":"Ell","year":"2014"},{"key":"10.1016\/j.cam.2026.117543_bib0029","series-title":"Quaternion Algebras","author":"Voight","year":"2021"},{"key":"10.1016\/j.cam.2026.117543_bib0030","series-title":"Hypercomplex Numbers: An Elementary Introduction to Algebras","volume":"302","author":"Kantor","year":"1989"},{"issue":"3","key":"10.1016\/j.cam.2026.117543_bib0031","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","article-title":"Tensor decompositions and applications","volume":"51","author":"Kolda","year":"2009","journal-title":"SIAM Rev."},{"issue":"3","key":"10.1016\/j.cam.2026.117543_bib0032","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.laa.2010.09.020","article-title":"Factorization strategies for third-order tensors","volume":"435","author":"Kilmer","year":"2011","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2026.117543_bib0033","series-title":"Signal Theory Methods in Multispectral Remote Sensing","volume":"29","author":"Landgrebe","year":"2005"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726002013?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726002013?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T10:57:39Z","timestamp":1773140259000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726002013"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":33,"alternative-id":["S0377042726002013"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117543","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Nested quaternion matrix and recursive approach to its singular value decomposition","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117543","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117543"}}