{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:26:23Z","timestamp":1760149583488,"version":"build-2065373602"},"reference-count":63,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T00:00:00Z","timestamp":1693180800000},"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":["1"],"award-info":[{"award-number":["1"]}],"id":[{"id":"10.13039\/501100012639","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein\u2013Vandermonde matrices, Bernstein\u2013Bezoutian structured matrices, Cauchy\u2014polynomial-Vandermonde structured matrices, and quasi-rational Bernstein\u2013Vandermonde structured matrices are well studied and investigated in the literature. We aim to present some new results for the numerical approximation of the largest singular values corresponding to Bernstein\u2013Vandermonde, Bernstein\u2013Bezoutian, Cauchy\u2014polynomial-Vandermonde and quasi-rational Bernstein\u2013Vandermonde structured matrices. The numerical approximation for the reciprocal of the largest singular values returns the structured singular values. The new results for the numerical approximation of bounds from below for structured singular values are accomplished by computing the largest singular values of totally positive Bernstein\u2013Vandermonde structured matrices, Bernstein\u2013Bezoutian structured matrices, Cauchy\u2014polynomial-Vandermonde structured matrices, and quasi-rational Bernstein\u2013Vandermonde structured matrices. Furthermore, we present the spectral properties of totally positive Bernstein\u2013Vandermonde structured matrices, Bernstein\u2013Bezoutian structured matrices, Cauchy\u2014polynomial-Vandermonde structured matrices, and structured quasi-rational Bernstein\u2013Vandermonde matrices by computing the eigenvalues, singular values, structured singular values and its lower and upper bounds and condition numbers.<\/jats:p>","DOI":"10.3390\/axioms12090831","type":"journal-article","created":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T08:59:05Z","timestamp":1693299545000},"page":"831","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Stability Analysis of Linear Systems with Cauchy\u2014Polynomial-Vandermonde Matrices"],"prefix":"10.3390","volume":"12","author":[{"given":"Mutti-Ur","family":"Rehman","sequence":"first","affiliation":[{"name":"Department of Mathematical Analysis, Bukhara State University, Bukhara 200100, Uzbekistan"}],"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 Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Department of Industrial Engineering, OST\u0130M Technical University, Ankara 06374, T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1511-9760","authenticated-orcid":false,"given":"Nahid","family":"Fatima","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tulkin H.","family":"Rasulov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis, Bukhara State University, Bukhara 200100, Uzbekistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"ref_1","unstructured":"James, D., Ioana, D., Olga, H., and Plamen, K. 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