{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T14:16:44Z","timestamp":1758637004438,"version":"3.37.3"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Problems in Engineering"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>Many zero-finding numerical methods are based on the Intermediate Value Theorem, which states that a zero of a real function is bracketed in a given interval if and have opposite signs; that is, . But, some zeros cannot be bracketed this way because they do not satisfy the precondition . For example, local minima and maxima that annihilate may not be bracketed by the Intermediate Value Theorem. In this case, we can always use a numerical method for bracketing extrema, checking then whether it is a zero of or not. Instead, this paper introduces a single numerical method, called<jats:italic>generalized regula falsi<\/jats:italic>(GRF) method to determine both zeros and extrema of a function. Consequently, it differs from the standard<jats:italic>regula falsi method<\/jats:italic>in that it is capable of finding any function zero in a given interval even when the Intermediate Value Theorem is not satisfied.<\/jats:p>","DOI":"10.1155\/2013\/394654","type":"journal-article","created":{"date-parts":[[2013,7,30]],"date-time":"2013-07-30T17:02:14Z","timestamp":1375203734000},"page":"1-9","source":"Crossref","is-referenced-by-count":4,"title":["A Generalized Regula Falsi Method for Finding Zeros and Extrema of Real Functions"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5804-5717","authenticated-orcid":true,"given":"Abel","family":"Gomes","sequence":"first","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, Universidade da Beira Interior, 6200-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9292-5323","authenticated-orcid":true,"given":"Jos\u00e9","family":"Morgado","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, Universidade da Beira Interior, 6200-001 Covilh\u00e3, Portugal"}]}],"member":"311","reference":[{"year":"1965","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/1019044"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/14.4.422"},{"year":"1992","key":"5"},{"issue":"1","key":"9","first-page":"1","volume":"4","year":"2013","journal-title":"International Journal of Experimental Algorithms"},{"issue":"1","key":"10","first-page":"21","volume":"2","year":"2011","journal-title":"International Journal of Experimental Algorithms"},{"year":"1978","series-title":"International Series in Pure and Applied Mathematics","key":"6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1979.1084580"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.09.052"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1080\/00207160601117339"}],"container-title":["Mathematical Problems in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/mpe\/2013\/394654.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/mpe\/2013\/394654.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/mpe\/2013\/394654.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T15:03:53Z","timestamp":1471532633000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/mpe\/2013\/394654\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":10,"alternative-id":["394654","394654"],"URL":"https:\/\/doi.org\/10.1155\/2013\/394654","relation":{},"ISSN":["1024-123X","1563-5147"],"issn-type":[{"type":"print","value":"1024-123X"},{"type":"electronic","value":"1563-5147"}],"subject":[],"published":{"date-parts":[[2013]]}}}