{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T11:12:01Z","timestamp":1760181121709,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T00:00:00Z","timestamp":1604448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012639","name":"Prince Sultan University","doi-asserted-by":"publisher","award":["RG-DES-2017-01-17"],"award-info":[{"award-number":["RG-DES-2017-01-17"]}],"id":[{"id":"10.13039\/501100012639","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For n-dimensional real-valued matrix A, the computation of nearest correlation matrix; that is, a symmetric, positive semi-definite, unit diagonal and off-diagonal entries between \u22121 and 1 is a problem that arises in the finance industry where the correlations exist between the stocks. The proposed methodology presented in this article computes the admissible perturbation matrix and a perturbation level to shift the negative spectrum of perturbed matrix to become non-negative or strictly positive. The solution to optimization problems constructs a gradient system of ordinary differential equations that turn over the desired perturbation matrix. Numerical testing provides enough evidence for the shifting of the negative spectrum and the computation of nearest correlation matrix.<\/jats:p>","DOI":"10.3390\/sym12111824","type":"journal-article","created":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T00:00:37Z","timestamp":1604534437000},"page":"1824","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Computing Nearest Correlation Matrix via Low-Rank ODE\u2019s Based Technique"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5828-3133","authenticated-orcid":false,"given":"Mutti-Ur","family":"Rehman","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan"},{"name":"Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5262-1138","authenticated-orcid":false,"given":"Jehad","family":"Alzabut","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0735-6520","authenticated-orcid":false,"given":"Kamaleldin","family":"Abodayeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,4]]},"reference":[{"key":"ref_1","first-page":"3","article-title":"A methodology to stress correlations","volume":"4","author":"Finger","year":"1997","journal-title":"RiskMetrics Monit."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0024-3795(88)90223-6","article-title":"Computing a nearest symmetric positive semidefinite matrix","volume":"103","author":"Higham","year":"1988","journal-title":"Linear Algebra Its Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.21314\/JOR.2003.081","article-title":"Correlation stress testing for value-at-risk","volume":"5","author":"Saygun","year":"2003","journal-title":"J. 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Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s10107-006-0088-y","article-title":"An inexact primal\u2013dual path following algorithm for convex quadratic SDP","volume":"112","author":"Toh","year":"2008","journal-title":"Math. Program."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1093\/imanum\/dru038","article-title":"Approximating real stability radii","volume":"35","author":"Guglielmi","year":"2015","journal-title":"IMA J. Numer. Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1824\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:28:55Z","timestamp":1760178535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1824"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,4]]},"references-count":11,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["sym12111824"],"URL":"https:\/\/doi.org\/10.3390\/sym12111824","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,11,4]]}}}