{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,8,7]],"date-time":"2022-08-07T09:47:25Z","timestamp":1659865645841},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[1970,10]]},"abstract":"\n Given\n N<\/jats:italic>\n approximations to the zeros of an\n N<\/jats:italic>\n th-degree polynomial,\n N<\/jats:italic>\n circular regions in the complex\n z<\/jats:italic>\n -plane are determined whose union contains all the zeros, and each connected component of this union consisting of\n K<\/jats:italic>\n such circular regions contains exactly\n K<\/jats:italic>\n zeros. The bounds for the zeros provided by these circular regions are not excessively pessimistic; that is, whenever the approximations are sufficiently well separated and sufficiently close to the zeros of this polynomial, the radii of these circular regions are shown to overestimate the errors by at most a modest factor simply related to the configuration of the approximations. A few numerical examples are included.\n <\/jats:p>","DOI":"10.1145\/321607.321615","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:26:10Z","timestamp":1027769170000},"page":"661-674","source":"Crossref","is-referenced-by-count":50,"title":["Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems"],"prefix":"10.1145","volume":"17","author":[{"given":"Brian T.","family":"Smith","sequence":"first","affiliation":[{"name":"Eidg. Technische Hochschule, Forschungsinstitut f\u00fcr Mathematik, Z\u00fcrich, Switzerland and University of Toronto, Department of Computer Science, Toronto, Ontario, Canada"}]}],"member":"320","reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1145\/363717.363775"},{"key":"e_1_2_1_2_2","first-page":"119","volume-title":"Oliver and Boyd","author":"AITKN A.C.","year":"1956"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1090\/S0002-9904-1915-02684-4","article-title":"An elementary double inequality for the roots of an algebraic equation having greatest absolute value","volume":"21","author":"BIRKOFF GE D","year":"1916","journal-title":"Bull. Amer. Math. Soe."},{"key":"e_1_2_1_4_2","first-page":"297","volume-title":"Green and Co.","author":"BURNSIDE W.S.","year":"1886"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF02165233","article-title":"Correcting approximations to multiple roots of polynomials","volume":"9","author":"DXNIELS J.W","year":"1966","journal-title":"Numer. Math."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/365559.365619"},{"key":"e_1_2_1_7_2","unstructured":"MXRDEN M. Geometry of Zeros. Amer. Math. Soc. Providence R. I. 1966. MXRDEN M. Geometry of Zeros. Amer. Math. Soc. Providence R. I. 1966."},{"key":"e_1_2_1_8_2","first-page":"67","volume-title":"Proc. 1967 Army Numerical Analysis Conference","author":"SMITH B.T.","year":"1967"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1080\/00029890.1960.11989446","article-title":"A generalization of Hermite's interpolation formula","volume":"67","author":"SPITZEXRT A","year":"1960","journal-title":"Amer. Math. Mon."},{"key":"e_1_2_1_11_2","unstructured":"STAFF INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF TORONTO. Programmer's Reference Manual for the IBM 7094-II Computer 2nd ed. Vol. II. University of Toronto Toronto Ontario 1968. STAFF INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF TORONTO. Programmer's Reference Manual for the IBM 7094-II Computer 2nd ed. Vol. II. University of Toronto Toronto Ontario 1968."},{"key":"e_1_2_1_12_2","first-page":"279","volume-title":"Todd, J., E d., A Survey of Numerical Analysis","author":"TAUSSKY O., .","year":"1962"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/355592.365600"}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/321607.321615","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T19:29:52Z","timestamp":1614713392000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/321607.321615"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1970,10]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1970,10]]}},"alternative-id":["10.1145\/321607.321615"],"URL":"http:\/\/dx.doi.org\/10.1145\/321607.321615","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":["Artificial Intelligence","Hardware and Architecture","Information Systems","Control and Systems Engineering","Software"],"published":{"date-parts":[[1970,10]]}}}