{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T16:57:23Z","timestamp":1781283443608,"version":"3.54.1"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"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":[[2026,12]]},"DOI":"10.1016\/j.cam.2026.117805","type":"journal-article","created":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T15:03:56Z","timestamp":1779807836000},"page":"117805","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Numerical approach for solving problems arising from polynomial analysis"],"prefix":"10.1016","volume":"488","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3943-1898","authenticated-orcid":false,"given":"Yousra","family":"Gati","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vladimir Petrov","family":"Kostov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohamed Chaouki","family":"Tarchi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.cam.2026.117805_bib0001","doi-asserted-by":"crossref","first-page":"21","DOI":"10.3390\/a19010021","article-title":"Adaptive parallel methods for polynomial equations with unknown multiplicity","volume":"19","author":"Shams","year":"2025","journal-title":"Algorithms"},{"issue":"11","key":"10.1016\/j.cam.2026.117805_bib0002","doi-asserted-by":"crossref","DOI":"10.1016\/j.asej.2025.103670","article-title":"Converging efficiency: computational and fractal insights into parallel non-linear schemes","volume":"16","author":"Shams","year":"2025","journal-title":"Ain Shams Eng. J."},{"key":"10.1016\/j.cam.2026.117805_bib0003","unstructured":"Y. Gati, V.P. Kostov, Midpoints and critical points, 2025. arXiv: 2512.07322."},{"key":"10.1016\/j.cam.2026.117805_bib0004","series-title":"The Geometry of Ren\u00e9 Descartes\u2019","author":"Smith","year":"1954"},{"key":"10.1016\/j.cam.2026.117805_bib0005","first-page":"181","article-title":"Sur l\u2019usage du th\u00e9or\u00e8me de descartes' dans la recherche des limites des racines","author":"Fourier","year":"1820","journal-title":"Bull. Sci. Par Soci\/\u2019Et\u2019e Philomatique Paris"},{"key":"10.1016\/j.cam.2026.117805_bib0006","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1080\/00029890.1999.12005131","article-title":"Descartes\u2019 rule of signs: another construction","volume":"106","author":"Grabiner","year":"1999","journal-title":"Am Math. Mon."},{"key":"10.1016\/j.cam.2026.117805_bib0007","doi-asserted-by":"crossref","first-page":"186","DOI":"10.4171\/em\/262","article-title":"Some remarks about Descartes\u2019 rule of signs","volume":"69","author":"Albouy","year":"2014","journal-title":"Elem. Math."},{"issue":"4","key":"10.1016\/j.cam.2026.117805_bib0008","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1080\/10586458.2015.1030051","article-title":"Could Ren\u00e9 Descartes\u2019 have known this?","volume":"24","author":"Forsg\u00e5rd","year":"2015","journal-title":"Exp. Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117805_bib0009","doi-asserted-by":"crossref","first-page":"853","DOI":"10.21136\/CMJ.2018.0163-17","article-title":"On realizability of sign patterns by real polynomials","volume":"68","author":"Kostov","year":"2018","journal-title":"Czech. Math. J."},{"key":"10.1016\/j.cam.2026.117805_bib0010","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1007\/s10986-020-09491-9","article-title":"On Descartes\u2019 rule for polynomials with two variations of sign","volume":"60","author":"Cheriha","year":"2020","journal-title":"Lith. Math. J."},{"issue":"1","key":"10.1016\/j.cam.2026.117805_bib0011","doi-asserted-by":"crossref","first-page":"39","DOI":"10.21136\/MB.2018.0091-17","article-title":"Polynomials, sign patterns and Descartes\u2019 rule of signs","volume":"144","author":"Kostov","year":"2019","journal-title":"Math. Bohem."},{"key":"10.1016\/j.cam.2026.117805_bib0012","doi-asserted-by":"crossref","first-page":"25","DOI":"10.60063\/gsu.fmi.106.25-51","article-title":"A nonrealization theorem in the context of Descartes\u2019 rule of signs","volume":"106","author":"Cheriha","year":"2019","journal-title":"Annu. Sofia Univ. \u201cSt Kliment Ohridski\u201d Fac. Math. Inf."},{"issue":"G8","key":"10.1016\/j.cam.2026.117805_bib0013","doi-asserted-by":"crossref","first-page":"863","DOI":"10.5802\/crmath.610","article-title":"Further than Descartes\u2019 rule of signs","volume":"362","author":"Gati","year":"2024","journal-title":"C. R. Math."},{"key":"10.1016\/j.cam.2026.117805_bib0014","series-title":"Polynomials - Theory and Application","article-title":"New aspects of Descartes\u2019 rule of signs","author":"Kostov","year":"2018"},{"issue":"2","key":"10.1016\/j.cam.2026.117805_bib0015","first-page":"128","article-title":"Beyond Descartes\u2019 rule of signs","volume":"6","author":"Kostov","year":"2023","journal-title":"Constr. Math. Anal."},{"key":"10.1016\/j.cam.2026.117805_bib0016","series-title":"Constructive Theory of Functions, Sozopol","article-title":"Moduli of roots of hyperbolic polynomials and Descartes\u2019 rule of signs","author":"Kostov","year":"2019"},{"issue":"2","key":"10.1016\/j.cam.2026.117805_bib0017","first-page":"163","article-title":"Degree 6 hyperbolic polynomials and orders of moduli","volume":"29","author":"Gati","year":"2024","journal-title":"Math. Commun."},{"issue":"1\u20132","key":"10.1016\/j.cam.2026.117805_bib0018","doi-asserted-by":"crossref","first-page":"161","DOI":"10.5486\/PMD.2020.8640","article-title":"Descartes\u2019 rule of signs and moduli of roots","volume":"96","author":"Kostov","year":"2020","journal-title":"Publ. Math. Debr."},{"key":"10.1016\/j.cam.2026.117805_bib0019","first-page":"60","article-title":"Sign patterns and rigid orders of moduli","volume":"6","author":"Gati","year":"2021","journal-title":"Graduate J. Math."},{"key":"10.1016\/j.cam.2026.117805_bib0020","article-title":"Topics on Hyperbolic Polynomials in One Variable","volume":"33","author":"Kostov","year":"2011"},{"key":"10.1016\/j.cam.2026.117805_bib0021","first-page":"135","article-title":"Hyperbolic polynomials and canonical sign patterns","volume":"46","author":"Kostov","year":"2020","journal-title":"Serdica Math. J."},{"issue":"1\u20132","key":"10.1016\/j.cam.2026.117805_bib0022","doi-asserted-by":"crossref","first-page":"119","DOI":"10.5486\/PMD.2022.9068","article-title":"Hyperbolic polynomials and rigid moduli orders","volume":"100","author":"Kostov","year":"2022","journal-title":"Publ. Math. Debr."},{"key":"10.1016\/j.cam.2026.117805_bib0023","series-title":"Probl\u00e8mes provenant de la r\u00e8gle de Descartes","author":"Tarchi","year":"2024"},{"key":"10.1016\/j.cam.2026.117805_bib0024","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.bulsci.2007.11.006","article-title":"Distances between critical points and midpoints of zeros of hyperbolic polynomials","volume":"134","author":"Dimitrov","year":"2010","journal-title":"Bull. Sci. math."},{"key":"10.1016\/j.cam.2026.117805_bib0025","doi-asserted-by":"crossref","first-page":"3789","DOI":"10.1090\/S0002-9947-05-03721-9","article-title":"Differentiation evens spacings","volume":"357","author":"Farmer","year":"2005","journal-title":"Trans. Amer. Math. Soc."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726004474?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726004474?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T16:12:00Z","timestamp":1781280720000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726004474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":25,"alternative-id":["S0377042726004474"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117805","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Numerical approach for solving problems arising from polynomial analysis","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.2026.117805","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":"117805"}}