{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:38:21Z","timestamp":1776785901859,"version":"3.51.2"},"reference-count":7,"publisher":"American Mathematical Society (AMS)","issue":"256","license":[{"start":{"date-parts":[[2007,6,28]],"date-time":"2007-06-28T00:00:00Z","timestamp":1182988800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We study an infinite family of lower and upper bounds on the modulus of zeros of complex polynomials derived by Kalantari. We first give a simple characterization of these bounds which leads to an efficient algorithm for their computation. For a polynomial of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    our algorithm computes the first\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m\">\n                        <mml:semantics>\n                          <mml:mi>m<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    bounds in Kalantari\u2019s family in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper O left-parenthesis m n right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">O(mn)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    operations. We further prove that for every complex polynomial these lower and upper bounds converge to the tightest annulus containing the roots, and thus settle a problem raised in Kalantari\u2019s paper.\n                  <\/p>","DOI":"10.1090\/s0025-5718-06-01868-0","type":"journal-article","created":{"date-parts":[[2006,8,16]],"date-time":"2006-08-16T10:28:45Z","timestamp":1155724125000},"page":"1905-1912","source":"Crossref","is-referenced-by-count":3,"title":["On efficient computation and asymptotic sharpness of Kalantari\u2019s bounds for zeros of polynomials"],"prefix":"10.1090","volume":"75","author":[{"given":"Yi","family":"Jin","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2006,6,28]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics","volume-title":"Applied and computational complex analysis","author":"Henrici, Peter","year":"1974"},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"267","DOI":"10.2307\/2690530","article-title":"A proof in the spirit of Zeilberger of an amazing identity of Ramanujan","volume":"69","author":"Hirschhorn, M. D.","year":"1996","journal-title":"Math. Mag.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-570X","issn-type":"print"},{"issue":"250","key":"3","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1090\/S0025-5718-04-01686-2","article-title":"An infinite family of bounds on zeros of analytic functions and relationship to Smale\u2019s bound","volume":"74","author":"Kalantari, Bahman","year":"2005","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1016\/S0377-0427(01)00546-5","article-title":"A 2002 update of the supplementary bibliography on roots of polynomials","volume":"142","author":"McNamee, John Michael","year":"2002","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"5","unstructured":"J. M. McNamee and M. Olhovsky, A comparison of a priori bounds on (real or complex) roots of polynomials, to appear in Proceedings of 17th IMACS World Congress, Paris, France, July 2005."},{"key":"6","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9171-5","volume-title":"Mathematics for computer algebra","author":"Mignotte, Maurice","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0387976752"},{"key":"7","isbn-type":"print","first-page":"100","article-title":"Generating functions","author":"Stanley, Richard P.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0883851172"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2006-75-256\/S0025-5718-06-01868-0\/S0025-5718-06-01868-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-256\/S0025-5718-06-01868-0\/S0025-5718-06-01868-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:41:14Z","timestamp":1776782474000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-256\/S0025-5718-06-01868-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6,28]]},"references-count":7,"journal-issue":{"issue":"256","published-print":{"date-parts":[[2006,10]]}},"alternative-id":["S0025-5718-06-01868-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-06-01868-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2006,6,28]]}}}