{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:43:54Z","timestamp":1750308234257,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2004,9,1]],"date-time":"2004-09-01T00:00:00Z","timestamp":1093996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[2004,9]]},"abstract":"<jats:p>\n            Let\n            <jats:italic>P<\/jats:italic>\n            (\n            <jats:italic>z<\/jats:italic>\n            ) be a univariate polynomial over\n            <jats:bold>C<\/jats:bold>\n            , having\n            <jats:italic>m<\/jats:italic>\n            close roots around the origin. We present a theorem which separates a cluster of\n            <jats:italic>m - k<\/jats:italic>\n            close roots of\n            <jats:italic>\n              d\n              <jats:sup>k<\/jats:sup>\n              P\n            <\/jats:italic>\n            \/d\n            <jats:italic>\n              z\n              <jats:sup>k<\/jats:sup>\n            <\/jats:italic>\n            around the origin from the other roots, where 0 \u2264\n            <jats:italic>k<\/jats:italic>\n            &lt;\n            <jats:italic>m<\/jats:italic>\n            . We compare our theorem with those of Marden-Walsh and Yakoubsohn, and show superiority of our theorem.\n          <\/jats:p>","DOI":"10.1145\/1040034.1040039","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"85-92","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A theorem for separating close roots of a polynomial and its derivatives"],"prefix":"10.1145","volume":"38","author":[{"given":"Tateaki","family":"Sasaki","sequence":"first","affiliation":[{"name":"University of Tsukuba, Tsukuba-shi, Ibaraki, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2004,9]]},"reference":[{"key":"e_1_2_1_1_1","series-title":"Mathematical Surveys","volume-title":"The Geometry of the Zeros of A Polynomial in a Complex Variable","author":"Marden M.","year":"1949","unstructured":"M. Marden . The Geometry of the Zeros of A Polynomial in a Complex Variable . Vol. 3 of Mathematical Surveys , AMS , New York , 1949 . M. Marden. The Geometry of the Zeros of A Polynomial in a Complex Variable. Vol. 3 of Mathematical Surveys, AMS, New York, 1949."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/121448"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(91)90180-R"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/70413.70420"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/603273.603277"},{"key":"e_1_2_1_6_1","volume-title":"Approximate zero-points\" of real univariate polynomial with large error terms","author":"Terui A.","year":"2000","unstructured":"A. Terui and T. Sasaki . \" Approximate zero-points\" of real univariate polynomial with large error terms . IPSJ Journal (Information Processing Society of Japan) 41 ( 2000 ), 974--989. A. Terui and T. Sasaki. \"Approximate zero-points\" of real univariate polynomial with large error terms. IPSJ Journal (Information Processing Society of Japan)41 (2000), 974--989."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.2000.0555"},{"key":"e_1_2_1_8_1","first-page":"433","article-title":"Simultaneous computation of all the zero-cluster of a univariate polynomial. In: Foundations of Computational Mathematics (eds","author":"Yakoubsohn J.-C.","year":"2002","unstructured":"J.-C. Yakoubsohn . Simultaneous computation of all the zero-cluster of a univariate polynomial. In: Foundations of Computational Mathematics (eds . F. Cucker and M. Rojas) ( 2002 ), 433 -- 457 . J.-C. Yakoubsohn. Simultaneous computation of all the zero-cluster of a univariate polynomial. In: Foundations of Computational Mathematics (eds. F. Cucker and M. Rojas) (2002), 433--457.","journal-title":"F. Cucker and M. Rojas) ("}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1040034.1040039","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1040034.1040039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:31:45Z","timestamp":1750264305000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1040034.1040039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,9]]}},"alternative-id":["10.1145\/1040034.1040039"],"URL":"https:\/\/doi.org\/10.1145\/1040034.1040039","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[2004,9]]},"assertion":[{"value":"2004-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}