{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T05:34:52Z","timestamp":1736573692255,"version":"3.32.0"},"publisher-location":"Berlin, Heidelberg","reference-count":34,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540388753"},{"type":"electronic","value":"9783540388760"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11841036_72","type":"book-chapter","created":{"date-parts":[[2006,9,11]],"date-time":"2006-09-11T13:20:54Z","timestamp":1157980854000},"page":"817-828","source":"Crossref","is-referenced-by-count":12,"title":["Univariate Polynomial Real Root Isolation: Continued Fractions Revisited"],"prefix":"10.1007","author":[{"given":"Elias P.","family":"Tsigaridas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis Z.","family":"Emiris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"72_CR1","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/BF01395988","volume":"36","author":"A. Akritas","year":"1980","unstructured":"Akritas, A.: An implementation of Vincent\u2019s theorem. Numerische Mathematik\u00a036, 53\u201362 (1980)","journal-title":"Numerische Mathematik"},{"key":"72_CR2","doi-asserted-by":"crossref","unstructured":"Akritas, A.: There is no \u201dUspensky\u2019s method\u201d. Extended Abstract. In: Proc. Symp. on Symbolic and Algebraic Computation, Waterloo, Canada, pp. 88\u201390 (1986)","DOI":"10.1145\/32439.32457"},{"key":"72_CR3","unstructured":"Akritas, A., Bocharov, A., Strz\u00e9bonski, A.: Implementation of real root isolation algorithms in Mathematica. In: Abstracts of Interval 1994, Russia, pp. 23\u201327 (1994)"},{"issue":"4","key":"72_CR4","doi-asserted-by":"crossref","first-page":"297","DOI":"10.15388\/NA.2005.10.4.15110","volume":"10","author":"A. Akritas","year":"2005","unstructured":"Akritas, A., Strzebonski, A.: A comparative study of two real root isolation methods. Nonlinear Analysis: Modelling and Control\u00a010(4), 297\u2013304 (2005)","journal-title":"Nonlinear Analysis: Modelling and Control"},{"key":"72_CR5","volume-title":"Elements of Computer Algebra with Applications","author":"A.G. Akritas","year":"1989","unstructured":"Akritas, A.G.: Elements of Computer Algebra with Applications. J. Wiley & Sons, New York (1989)"},{"key":"72_CR6","doi-asserted-by":"crossref","unstructured":"Bini, D., Fiorentino, G.: Design, analysis, and implementation of a multiprecision polynomial rootfinder. Numerical Algorithms, 127\u2013173 (2000)","DOI":"10.1023\/A:1019199917103"},{"key":"72_CR7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/978-94-017-1108-1_10","volume-title":"Computational Algebra and Number Theory","author":"E. Bombieri","year":"1995","unstructured":"Bombieri, E., van der Poorten, A.: Continued fractions of algebraic numbers. In: Computational Algebra and Number Theory, pp. 137\u2013152. Kluwer, Dordrecht (1995)"},{"key":"72_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/3-540-61581-4_39","volume-title":"Algorithmic Number Theory","author":"R. Brent","year":"1996","unstructured":"Brent, R., van der Poorten, A., Riele, H.: A comparative study of algorithms for computing continued fractions of algebraic numbers. In: Cohen, H. (ed.) ANTS 1996. LNCS, vol.\u00a01122, pp. 35\u201347. Springer, Heidelberg (1996)"},{"key":"72_CR9","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1145\/800205.806346","volume-title":"SYMSAC 1976","author":"G. Collins","year":"1976","unstructured":"Collins, G., Akritas, A.: Polynomial real root isolation using Descartes\u2019 rule of signs. In: SYMSAC 1976, New York, USA, pp. 272\u2013275. ACM Press, New York (1976)"},{"key":"72_CR10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/978-3-7091-3406-1_7","volume-title":"Computer Algebra: Symbolic and Algebraic Computation","author":"G.E. Collins","year":"1982","unstructured":"Collins, G.E., Loos, R.: Real zeros of polynomials. In: Buchberger, B., Collins, G.E., Loos, R. (eds.) Computer Algebra: Symbolic and Algebraic Computation, 2nd edn., pp. 83\u201394. Springer, Wien (1982)","edition":"2"},{"key":"72_CR11","unstructured":"Davenport, J.H.: Cylindrical algebraic decomposition. Technical Report 88\u201310, School of Mathematical Sciences, University of Bath, England (1988)"},{"key":"72_CR12","unstructured":"Du, Z., Sharma, V., Yap, C.K.: Amortized bound for root isolation via Sturm sequences. In: Wang, D., Zhi, L. (eds.) Int. Workshop on Symbolic Numeric Computing, School of Science, Beihang University, Beijing, China, pp. 81\u201393 (2005)"},{"key":"72_CR13","unstructured":"Eigenwillig, A., Sharma, V., Yap, C.: Almost tight complexity bounds for the Descartes method. In: ISSAC 2006 (to appear, 2006)"},{"key":"72_CR14","unstructured":"Emiris, I., Tsigaridas, E.P.: Computations with one and two algebraic numbers. Technical report, ArXiv (December 2005)"},{"key":"72_CR15","unstructured":"Emiris, I.Z., Mourrain, B., Tsigaridas, E.P.: Real Algebraic Numbers: Complexity Analysis and Experimentation. RR 5897, INRIA (April 2006)"},{"key":"72_CR16","doi-asserted-by":"crossref","unstructured":"Emiris, I.Z., Tsigaridas, E.P., Tzoumas, G.M.: The predicates for the Voronoi diagram of ellipses. In: Proc. 24th Annual ACM SoCG, pp. 227\u2013236 (2006)","DOI":"10.1145\/1137856.1137891"},{"key":"72_CR17","volume-title":"Continued Fractions","author":"A. Khintchine","year":"1964","unstructured":"Khintchine, A.: Continued Fractions. University of Chicago Press, Chicago (1964)"},{"key":"72_CR18","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/0377-0427(86)90096-8","volume":"16","author":"J. Kioustelidis","year":"1986","unstructured":"Kioustelidis, J.: Bounds for the positive roots of polynomials. Journal of Computational and Applied Mathematics\u00a016, 241\u2013244 (1986)","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"1","key":"72_CR19","first-page":"49","volume":"41","author":"W. Krandick","year":"2006","unstructured":"Krandick, W., Mehlhorn, K.: New bounds for the Descartes method. JSC\u00a041(1), 49\u201366 (2006)","journal-title":"JSC"},{"key":"72_CR20","volume-title":"Mathematics for computer algebra","author":"M. Mignotte","year":"1991","unstructured":"Mignotte, M.: Mathematics for computer algebra. Springer, New York (1991)"},{"key":"72_CR21","volume-title":"Polynomials","author":"M. Mignotte","year":"1999","unstructured":"Mignotte, M., Stefanescu, D.: Polynomials. Springer, Heidelberg (1999)"},{"issue":"6","key":"72_CR22","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/BF01198012","volume":"6","author":"M. Mignotte","year":"1995","unstructured":"Mignotte, M.: On the Distance Between the Roots of a Polynomial. Appl. Algebra Eng. Commun. Comput.\u00a06(6), 327\u2013332 (1995)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"72_CR23","unstructured":"Mourrain, B., Pavone, J.P., Tr\u00e9buchet, P., Tsigaridas, E.: SYNAPS, a library for symbolic-numeric computation. In: 8th MEGA, Italy. Software presentation (2005)"},{"issue":"2","key":"72_CR24","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1137\/S0036144595288554","volume":"39","author":"V. Pan","year":"1997","unstructured":"Pan, V.: Solving a polynomial equation: Some history and recent progress. SIAM Rev.\u00a039(2), 187\u2013220 (1997)","journal-title":"SIAM Rev."},{"key":"72_CR25","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1007\/BF01386297","volume":"4","author":"R. Richtmyer","year":"1962","unstructured":"Richtmyer, R., Devaney, M., Metropolis, N.: Continued fraction expansions of algebraic numbers. Numerische Mathematik\u00a04, 64\u201368 (1962)","journal-title":"Numerische Mathematik"},{"key":"72_CR26","doi-asserted-by":"publisher","first-page":"112","DOI":"10.2307\/2690148","volume":"51","author":"D. Rosen","year":"1978","unstructured":"Rosen, D., Shallit, J.: A continued fraction algorithm for approximating all real polynomial roots. Math. Mag.\u00a051, 112\u2013116 (1978)","journal-title":"Math. Mag."},{"issue":"1","key":"72_CR27","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.cam.2003.08.015","volume":"162","author":"F. Rouillier","year":"2004","unstructured":"Rouillier, F., Zimmermann, Z.: Efficient isolation of polynomial\u2019s real roots. J. of Computational and Applied Mathematics\u00a0162(1), 33\u201350 (2004)","journal-title":"J. of Computational and Applied Mathematics"},{"issue":"12","key":"72_CR28","first-page":"2132","volume":"11","author":"D. Stefanescu","year":"2005","unstructured":"Stefanescu, D.: New bounds for the positive roots of polynomials. Journal of Universal Computer Science\u00a011(12), 2132\u20132141 (2005)","journal-title":"Journal of Universal Computer Science"},{"key":"72_CR29","volume-title":"Theory of Equations","author":"J.V. Uspensky","year":"1948","unstructured":"Uspensky, J.V.: Theory of Equations. McGraw-Hill, New York (1948)"},{"key":"72_CR30","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1017\/CBO9780511721304.007","volume-title":"Diophantine analysis","author":"A. Poorten van der","year":"1986","unstructured":"van der Poorten, A.: An introduction to continued fractions. In: Diophantine analysis, pp. 99\u2013138. Cambridge University Press, Cambridge (1986)"},{"key":"72_CR31","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1007\/BF02168974","volume":"15","author":"A. Sluis van der","year":"1970","unstructured":"van der Sluis, A.: Upper bounds for the roots of polynomials. Numerische Mathematik\u00a015, 250\u2013262 (1970)","journal-title":"Numerische Mathematik"},{"key":"72_CR32","first-page":"341","volume":"1","author":"A.J.H. Vincent","year":"1836","unstructured":"Vincent, A.J.H.: Sur la r\u00e9solution des \u00e9quations num\u00e9riques. J. Math. Pures Appl.\u00a01, 341\u2013372 (1836)","journal-title":"J. Math. Pures Appl."},{"key":"72_CR33","doi-asserted-by":"crossref","unstructured":"von zur Gathen, J., Gerhard, J.: Fast Algorithms for Taylor Shifts and Certain Difference Equations. In: ISSAC, pp. 40\u201347 (1997)","DOI":"10.1145\/258726.258745"},{"key":"72_CR34","volume-title":"Fundamental Problems of Algorithmic Algebra","author":"C.K. Yap","year":"2000","unstructured":"Yap, C.K.: Fundamental Problems of Algorithmic Algebra. Oxford University Press, New York (2000)"}],"container-title":["Lecture Notes in Computer Science","Algorithms \u2013 ESA 2006"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11841036_72.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T20:33:19Z","timestamp":1736541199000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11841036_72"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540388753","9783540388760"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/11841036_72","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2006]]}}}