{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T14:49:57Z","timestamp":1743000597804,"version":"3.40.3"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031147876"},{"type":"electronic","value":"9783031147883"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-14788-3_1","type":"book-chapter","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T14:24:42Z","timestamp":1660141482000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Survey on\u00a0Generalizations of\u00a0the\u00a0Intermediate Value Theorem and\u00a0Applications"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8357-7435","authenticated-orcid":false,"given":"Michael N.","family":"Vrahatis","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,11]]},"reference":[{"key":"1_CR1","first-page":"102","volume":"17","author":"G Alefeld","year":"2004","unstructured":"Alefeld, G., Frommer, A., Heindl, G., Mayer, J.: On the existence theorems of Kantorovich, Miranda and Borsuk. Electron. Trans. Numer. Anal. 17, 102\u2013111 (2004)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"1_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112702","volume":"371","author":"B B\u00e1nhelyi","year":"2020","unstructured":"B\u00e1nhelyi, B., Csendes, T., Hatvan, L.: On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum. J. Comput. Appl. Math. 371, 112702 (2020)","journal-title":"J. Comput. Appl. Math."},{"key":"1_CR3","unstructured":"Bolzano, B.: Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwei Werten, die ein entgegengesetztes Resultat gew\u00e4hren, wenigstens eine reelle Wurzel der Gleichung liege. Prague (1817)"},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/S0304-3975(98)00101-7","volume":"210","author":"H Br\u00f6nnimann","year":"1999","unstructured":"Br\u00f6nnimann, H., Emiris, I.Z., Pan, V., Pion, S.: Sign determination in residue number systems. Theor. Comput. Sci. 210, 173\u2013197 (1999)","journal-title":"Theor. Comput. Sci."},{"key":"1_CR5","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BF01456931","volume":"71","author":"LEJ Brouwer","year":"1912","unstructured":"Brouwer, L.E.J.: \u00dcber Abbildungen von Mannigfaltigkeiten. Math. Ann. 71, 97\u2013115 (1912)","journal-title":"Math. Ann."},{"key":"1_CR6","unstructured":"Cauchy, A.-L.: Cours d\u2019Analyse de l\u2019\u00c9cole Royale Polytechnique, Paris (1821). (Reprinted in Oeuvres Completes, Series 2, vol. 3)"},{"issue":"1","key":"1_CR7","doi-asserted-by":"publisher","first-page":"1206","DOI":"10.1103\/PhysRevE.53.1206","volume":"53","author":"L Drossos","year":"1996","unstructured":"Drossos, L., Ragos, O., Vrahatis, M.N., Bountis, T.C.: Method for computing long periodic orbits of dynamical systems. Phys. Rev. E 53(1), 1206\u20131211 (1996)","journal-title":"Phys. Rev. E"},{"key":"1_CR8","unstructured":"Emiris I.Z., Mourrain B., Vrahatis M.N.: Sign methods for counting and computing real roots of algebraic systems. RR-3669, Inria (1999). inria-00073003"},{"key":"1_CR9","unstructured":"Emiris I.Z., Mourrain B., Vrahatis M.N.: Sign methods for enumerating solutions of nonlinear algebraic systems. In: Proceedings of the Fifth Hellenic European Conference on Computer Mathematics and Its Applications, vol. 2, pp. 469\u2013473, Athens, Greece (2002)"},{"key":"1_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0983-6","volume-title":"Chaos in Classical and Quantum Mechanics","author":"MC Gutzwiller","year":"1990","unstructured":"Gutzwiller, M.C.: Chaos in Classical and Quantum Mechanics. Springer, New York (1990). https:\/\/doi.org\/10.1007\/978-1-4612-0983-6"},{"key":"1_CR11","first-page":"109","volume":"21","author":"G Heindl","year":"2016","unstructured":"Heindl, G.: Generalizations of theorems of Rohn and Vrahatis. Reliable Comput. 21, 109\u2013116 (2016)","journal-title":"Reliable Comput."},{"key":"1_CR12","unstructured":"Jarn\u00edk, V.: Bernard Bolzano and the foundations of mathematical analysis. In: Bolzano and the Foundations of Mathematical Analysis, pp. 33\u201342. Society of Czechoslovak Mathematicians and Physicists, Prague (1981)"},{"issue":"144","key":"1_CR13","first-page":"1147","volume":"32","author":"RB Kearfott","year":"1978","unstructured":"Kearfott, R.B.: A proof of convergence and an error bound for the method of bisection in $$\\mathbb{R} ^n$$. Math. Comp. 32(144), 1147\u20131153 (1978)","journal-title":"Math. Comp."},{"key":"1_CR14","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/BF01404868","volume":"32","author":"RB Kearfott","year":"1979","unstructured":"Kearfott, R.B.: An efficient degree-computation method for a generalized method of bisection. Numer. Math. 32, 109\u2013127 (1979). https:\/\/doi.org\/10.1007\/BF01404868","journal-title":"Numer. Math."},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"132","DOI":"10.4064\/fm-14-1-132-137","volume":"14","author":"B Knaster","year":"1929","unstructured":"Knaster, B., Kuratowski, K., Mazurkiewicz, S.: Ein Beweis des Fixpunkt-satzes f\u00fcr $$n$$-dimensionale Simplexe. Fund. Math. 14, 132\u2013137 (1929)","journal-title":"Fund. Math."},{"issue":"1","key":"1_CR16","doi-asserted-by":"publisher","first-page":"219","DOI":"10.3982\/ECTA12536","volume":"86","author":"P Milgrom","year":"2018","unstructured":"Milgrom, P., Mollner, J.: Equilibrium selection in auctions and high stakes games. Econometrica 86(1), 219\u2013261 (2018)","journal-title":"Econometrica"},{"key":"1_CR17","unstructured":"Miranda, C.: Un\u2019 osservatione su un theorema di Brouwer. Bollettino dell\u2019U.M.I. 3, 5\u20137 (1940)"},{"issue":"2","key":"1_CR18","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1006\/jcom.2001.0636","volume":"18","author":"B Mourrain","year":"2002","unstructured":"Mourrain, B., Vrahatis, M.N., Yakoubsohn, J.C.: On the complexity of isolating real roots and computing with certainty the topological degree. J. Complex. 18(2), 612\u2013640 (2002)","journal-title":"J. Complex."},{"key":"1_CR19","doi-asserted-by":"crossref","unstructured":"Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Classics in Applied Mathematics vol. 30. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2000)","DOI":"10.1137\/1.9780898719468"},{"key":"1_CR20","first-page":"251","volume":"91","author":"H Poincar\u00e9","year":"1883","unstructured":"Poincar\u00e9, H.: Sur certaines solutions particuli\u00e8res du probl\u00e8me des trois corps. Comptes rendus de l\u2019Acad\u00e9mie des Sciences Paris 91, 251\u2013252 (1883)","journal-title":"Comptes rendus de l\u2019Acad\u00e9mie des Sciences Paris"},{"key":"1_CR21","first-page":"63","volume":"1","author":"H Poincar\u00e9","year":"1884","unstructured":"Poincar\u00e9, H.: Sur certaines solutions particuli\u00e8res du probl\u00e8me des trois corps. Bull. Astronomique 1, 63\u201374 (1884)","journal-title":"Bull. Astronomique"},{"key":"1_CR22","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF01459080","volume":"40","author":"K Sikorski","year":"1982","unstructured":"Sikorski, K.: Bisection is optimal. Numer. Math. 40, 111\u2013117 (1982)","journal-title":"Numer. Math."},{"key":"1_CR23","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780195106909.001.0001","volume-title":"Optimal Solution of Nonlinear Equations","author":"K Sikorski","year":"2001","unstructured":"Sikorski, K.: Optimal Solution of Nonlinear Equations. Oxford University Press, New York (2001)"},{"key":"1_CR24","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/BF02940617","volume":"6","author":"E Sperner","year":"1928","unstructured":"Sperner, E.: Neuer Beweis f\u00fcr die Invarianz der Dimensionszahl und des Gebietes. Abh. Math. Sem. Hamburg 6, 265\u2013272 (1928)","journal-title":"Abh. Math. Sem. Hamburg"},{"key":"1_CR25","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF01419526","volume":"25","author":"F Stenger","year":"1975","unstructured":"Stenger, F.: Computing the topological degree of a mapping in $$\\mathbb{R} ^n$$. Numer. Math. 25, 23\u201338 (1975)","journal-title":"Numer. Math."},{"key":"1_CR26","first-page":"161","volume":"27","author":"MN Vrahatis","year":"1986","unstructured":"Vrahatis, M.N.: An error estimation for the method of bisection in $$\\mathbb{R} ^n$$. Bull. Greek Math. Soc. 27, 161\u2013174 (1986)","journal-title":"Bull. Greek Math. Soc."},{"key":"1_CR27","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1145\/50063.214384","volume":"14","author":"MN Vrahatis","year":"1988","unstructured":"Vrahatis, M.N.: Solving systems of nonlinear equations using the nonzero value of the topological degree. ACM Trans. Math. Softw. 14, 312\u2013329 (1988)","journal-title":"ACM Trans. Math. Softw."},{"key":"1_CR28","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1145\/50063.51906","volume":"14","author":"MN Vrahatis","year":"1988","unstructured":"Vrahatis, M.N.: CHABIS: a mathematical software package for locating and evaluating roots of systems of nonlinear equations. ACM Trans. Math. Softw. 14, 330\u2013336 (1988)","journal-title":"ACM Trans. Math. Softw."},{"key":"1_CR29","first-page":"1","volume":"29","author":"MN Vrahatis","year":"1988","unstructured":"Vrahatis, M.N.: A variant of Jung\u2019s theorem. Bull. Greek Math. Soc. 29, 1\u20136 (1988)","journal-title":"Bull. Greek Math. Soc."},{"key":"1_CR30","first-page":"701","volume":"107","author":"MN Vrahatis","year":"1989","unstructured":"Vrahatis, M.N.: A short proof and a generalization of Miranda\u2019s existence theorem. Proc. Amer. Math. Soc. 107, 701\u2013703 (1989)","journal-title":"Proc. Amer. Math. Soc."},{"key":"1_CR31","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1006\/jcph.1995.1119","volume":"119","author":"MN Vrahatis","year":"1995","unstructured":"Vrahatis, M.N.: An efficient method for locating and computing periodic orbits of nonlinear mappings. J. Comput. Phys. 119, 105\u2013119 (1995)","journal-title":"J. Comput. Phys."},{"key":"1_CR32","first-page":"171","volume":"44","author":"MN Vrahatis","year":"2000","unstructured":"Vrahatis, M.N.: Simplex bisection and Sperner simplices. Bull. Greek Math. Soc. 44, 171\u2013180 (2000)","journal-title":"Bull. Greek Math. Soc."},{"key":"1_CR33","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.topol.2015.12.066","volume":"202","author":"MN Vrahatis","year":"2016","unstructured":"Vrahatis, M.N.: Generalization of the Bolzano theorem for simplices. Topol. Appl. 202, 40\u201346 (2016)","journal-title":"Topol. Appl."},{"key":"1_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2019.107036","volume":"275","author":"MN Vrahatis","year":"2020","unstructured":"Vrahatis, M.N.: Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros. Topol. Appl. 275, 107036 (2020)","journal-title":"Topol. Appl."},{"key":"1_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-3-030-40616-5_17","volume-title":"Numerical Computations: Theory and Algorithms","author":"MN Vrahatis","year":"2020","unstructured":"Vrahatis, M.N.: Generalizations of the intermediate value theorem for approximating fixed points and zeros of continuous functions. In: Sergeyev, Y.D., Kvasov, D.E. (eds.) NUMTA 2019, Part II. LNCS, vol. 11974, pp. 223\u2013238. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-40616-5_17"},{"key":"1_CR36","doi-asserted-by":"publisher","first-page":"1425","DOI":"10.1142\/S0218127496000849","volume":"6","author":"MN Vrahatis","year":"1996","unstructured":"Vrahatis, M.N., Bountis, T.C., Kollmann, M.: Periodic orbits and invariant surfaces of 4D nonlinear mappings. Int. J. Bifurcat. Chaos 6, 1425\u20131437 (1996)","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"1_CR37","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/BF01389620","volume":"49","author":"MN Vrahatis","year":"1986","unstructured":"Vrahatis, M.N., Iordanidis, K.I.: A rapid generalized method of bisection for solving systems of non-linear equations. Numer. Math. 49, 123\u2013138 (1986). https:\/\/doi.org\/10.1007\/BF01389620","journal-title":"Numer. Math."},{"key":"1_CR38","doi-asserted-by":"publisher","first-page":"2707","DOI":"10.1142\/S0218127497001825","volume":"7","author":"MN Vrahatis","year":"1997","unstructured":"Vrahatis, M.N., Isliker, H., Bountis, T.C.: Structure and breakdown of invariant tori in a 4D mapping model of accelerator dynamics. Int. J. Bifurcat. Chaos 7, 2707\u20132722 (1997)","journal-title":"Int. J. Bifurcat. Chaos"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-14788-3_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T23:14:53Z","timestamp":1660259693000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-14788-3_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031147876","9783031147883"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-14788-3_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"11 August 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Gebze","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Turkey","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 August 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 August 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"32","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"20","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"63% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.25","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5.1","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}